 9.2.1: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.2: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.3: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.4: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.5: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.6: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.7: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.8: Complete each trinomial so that it is a perfect square. Then factor...
 9.2.9: Which step is an appropriate way to begin solving the quadratic equ...
 9.2.10: In Example 3 of Section 6.5, we solved the quadratic equation 4p2 +...
 9.2.11: Solve each equation by completing the square. See Examples 2 and 3x...
 9.2.12: Solve each equation by completing the square. See Examples 2 and 3p...
 9.2.13: Solve each equation by completing the square. See Examples 2 and 3x...
 9.2.14: Solve each equation by completing the square. See Examples 2 and 3r...
 9.2.15: Solve each equation by completing the square. See Examples 2 and 3x...
 9.2.16: Solve each equation by completing the square. See Examples 2 and 3m...
 9.2.17: Solve each equation by completing the square. See Examples 2 and 3x...
 9.2.18: Solve each equation by completing the square. See Examples 2 and 32...
 9.2.19: Solve each equation by completing the square. See Examples 47.4x2 +...
 9.2.20: Solve each equation by completing the square. See Examples 47.9x2 4...
 9.2.21: Solve each equation by completing the square. See Examples 47.2p2 9...
 9.2.22: Solve each equation by completing the square. See Examples 47.3q2 ...
 9.2.23: Solve each equation by completing the square. See Examples 47.3x2 3...
 9.2.24: Solve each equation by completing the square. See Examples 47.6x2 3...
 9.2.25: Solve each equation by completing the square. See Examples 47.3x2 +...
 9.2.26: Solve each equation by completing the square. See Examples 47.2x2 3...
 9.2.27: Solve each equation by completing the square. See Examples 47.1x + ...
 9.2.28: Solve each equation by completing the square. See Examples 47.1x  ...
 9.2.29: Solve each equation by completing the square. See Examples 47.r  3...
 9.2.30: Solve each equation by completing the square. See Examples 47.1x  ...
 9.2.31: Solve each equation by completing the square. See Examples 47.x2 +...
 9.2.32: Solve each equation by completing the square. See Examples 47.2 x...
 9.2.33: Solve each equation by completing the square. Give (a) exact soluti...
 9.2.34: Solve each equation by completing the square. Give (a) exact soluti...
 9.2.35: Solve each equation by completing the square. Give (a) exact soluti...
 9.2.36: Solve each equation by completing the square. Give (a) exact soluti...
 9.2.37: Solve each problem. See Example 8.If an object is projected upward ...
 9.2.38: Solve each problem. See Example 8.After how many seconds will the o...
 9.2.39: Solve each problem. See Example 8.If an object is projected upward ...
 9.2.40: Solve each problem. See Example 8.At what times will the object des...
 9.2.41: Solve each problem. See Example 8.A farmer has a rectangular cattle...
 9.2.42: Solve each problem. See Example 8.The base of a triangle measures 1...
 9.2.43: Solve each problem. See Example 8.Two cars travel at right angles t...
 9.2.44: Solve each problem. See Example 8.Two painters are painting a house...
 9.2.45: Work Exercises 4548 in order.What is the area of the original square?
 9.2.46: Work Exercises 4548 in order.What is the area of the figure after t...
 9.2.47: Work Exercises 4548 in order.What is the area of the figure after t...
 9.2.48: Work Exercises 4548 in order.At what point did we complete the square?
 9.2.49: Write each quotient in lowest terms. Simplify the radicals. See Sec...
 9.2.50: Write each quotient in lowest terms. Simplify the radicals. See Sec...
 9.2.51: Write each quotient in lowest terms. Simplify the radicals. See Sec...
 9.2.52: Write each quotient in lowest terms. Simplify the radicals. See Sec...
 9.2.53: Evaluate the expression 2b2  4ac for the given values of a, b, and...
 9.2.54: Evaluate the expression 2b2  4ac for the given values of a, b, and...
Solutions for Chapter 9.2: Solving Quadratic Equations by Completing the Square
Full solutions for Beginning Algebra  11th Edition
ISBN: 9780321673480
Solutions for Chapter 9.2: Solving Quadratic Equations by Completing the Square
Get Full SolutionsThis textbook survival guide was created for the textbook: Beginning Algebra, edition: 11. Since 54 problems in chapter 9.2: Solving Quadratic Equations by Completing the Square have been answered, more than 40178 students have viewed full stepbystep solutions from this chapter. Chapter 9.2: Solving Quadratic Equations by Completing the Square includes 54 full stepbystep solutions. Beginning Algebra was written by and is associated to the ISBN: 9780321673480. This expansive textbook survival guide covers the following chapters and their solutions.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).