AI Tutor
Back to Intermediate Algebra 2e

9.2 Solve Quadratic Equations by Completing the Square

Adding (b/2)^2 to turn x^2 + bx into a perfect-square trinomial, and dividing out a leading coefficient first when one is present.

Intermediate Algebra 2e, 9.2 Solve Quadratic Equations by Completing the Square

Status
FlagsLoading your progress…

44 exercises

9.2 Exercise 1

Before you get started, take this readiness quiz.

Expand: (x+9)2.\left(x + 9\right)^{2} .
If you missed this problem, review the reference.

2.5

9.2 Exercise 2

Factor y2−14y+49.y^{2} - 14 y + 49 .
If you missed this problem, review the reference.

2.5

9.2 Exercise 3

Factor 5n2+40n+80.5 n^{2} + 40 n + 80 .
If you missed this problem, review the reference.

2.5

9.2 Exercise 5

Complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

ⓐ a2−20aa^{2} - 20 a ⓑ m2−5mm^{2} - 5 m ⓒ p2+14pp^{2} + \frac{1}{4} p

2.5

9.2 Exercise 6

Complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

ⓐ b2−4bb^{2} - 4 b ⓑ n2+13nn^{2} + 13 n ⓒ q2−23qq^{2} - \frac{2}{3} q

2.5

9.2 Exercise 8

Solve by completing the square: x2+4x=5.x^{2} + 4 x = 5 .

2.5

9.2 Exercise 9

Solve by completing the square: y2−10y=−9.y^{2} - 10 y = −9 .

2.5

9.2 Exercise 11

Solve by completing the square: y2−10y=−35.y^{2} - 10 y = −35 .

2.5

9.2 Exercise 12

Solve by completing the square: z2+8z=−19.z^{2} + 8 z = −19 .

2.5

9.2 Exercise 14

Solve by completing the square: x2−16x=−16.x^{2} - 16 x = −16 .

2.5

9.2 Exercise 15

Solve by completing the square: y2+8y=11.y^{2} + 8 y = 11 .

2.5

9.2 Exercise 17

Solve by completing the square: a2+4a+9=30.a^{2} + 4 a + 9 = 30 .

2.5

9.2 Exercise 18

Solve by completing the square: b2+8b−4=16.b^{2} + 8 b - 4 = 16 .

2.5

9.2 Exercise 20

Solve by completing the square: p2=5p+9.p^{2} = 5 p + 9 .

2.5

9.2 Exercise 21

Solve by completing the square: q2=7q−3.q^{2} = 7 q - 3 .

2.5

9.2 Exercise 23

Solve by completing the square: (c−2)(c+8)=11.\left(c - 2\right) \left(c + 8\right) = 11 .

2.5

9.2 Exercise 24

Solve by completing the square: (d−7)(d+3)=56.\left(d - 7\right) \left(d + 3\right) = 56 .

2.5

9.2 Exercise 26

Solve by completing the square: 2m2+16m+14=0.2 m^{2} + 16 m + 14 = 0 .

2.5

9.2 Exercise 27

Solve by completing the square: 4n2−24n−56=8.4 n^{2} - 24 n - 56 = 8 .

2.5

9.2 Exercise 29

Solve by completing the square: 3r2−2r=21.3 r^{2} - 2 r = 21 .

2.5

9.2 Exercise 30

Solve by completing the square: 4t2+2t=20.4 t^{2} + 2 t = 20 .

2.5

9.2 Exercise 32

Solve by completing the square: 4x2+3x=2.4 x^{2} + 3 x = 2 .

2.5

9.2 Exercise 33

Solve by completing the square: 3y2−10y=−5.3 y^{2} - 10 y = −5 .

2.5

9.2 Exercise 34

Complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

ⓐ m2−24mm^{2} - 24 m ⓑ x2−11xx^{2} - 11 x ⓒ p2−13pp^{2} - \frac{1}{3} p

2.5

9.2 Exercise 36

Complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

ⓐ p2−22pp^{2} - 22 p ⓑ y2+5yy^{2} + 5 y ⓒ m2+25mm^{2} + \frac{2}{5} m

2.5

9.2 Exercise 38

Solve by completing the square.

u2+2u=3u^{2} + 2 u = 3

2.5

9.2 Exercise 40

Solve by completing the square.

x2−20x=21x^{2} - 20 x = 21

2.5

9.2 Exercise 42

Solve by completing the square.

m2+4m=−44m^{2} + 4 m = −44

2.5

9.2 Exercise 44

Solve by completing the square.

r2+6r=−11r^{2} + 6 r = −11

2.5

9.2 Exercise 46

Solve by completing the square.

a2−10a=−5a^{2} - 10 a = −5

2.5

9.2 Exercise 48

Solve by completing the square.

x2+5x=2x^{2} + 5 x = 2

2.5

9.2 Exercise 50

Solve by completing the square.

u2−14u+12=−1u^{2} - 14 u + 12 = −1

2.5

9.2 Exercise 52

Solve by completing the square.

r2−4r−3=9r^{2} - 4 r - 3 = 9

2.5

9.2 Exercise 54

Solve by completing the square.

v2=9v+2v^{2} = 9 v + 2

2.5

9.2 Exercise 56

Solve by completing the square.

x2−5=10xx^{2} - 5 = 10 x

2.5

9.2 Exercise 58

Solve by completing the square.

(x+6)(x−2)=9\left(x + 6\right) \left(x - 2\right) = 9

2.5

9.2 Exercise 60

Solve by completing the square.

(x+2)(x+4)=3\left(x + 2\right) \left(x + 4\right) = 3

2.5

9.2 Exercise 62

Solve by completing the square.

3m2+30m−27=63 m^{2} + 30 m - 27 = 6

2.5

9.2 Exercise 64

Solve by completing the square.

2n2+4n=262 n^{2} + 4 n = 26

2.5

9.2 Exercise 66

Solve by completing the square.

2c2+c=62 c^{2} + c = 6

2.5

9.2 Exercise 68

Solve by completing the square.

2x2+7x−15=02 x^{2} + 7 x - 15 = 0

2.5

9.2 Exercise 70

Solve by completing the square.

2p2+7p=142 p^{2} + 7 p = 14

2.5

9.2 Exercise 72

Solve by completing the square.

5x2−3x=−105 x^{2} - 3 x = −10

2.5

9.2 Exercise 74

Solve the equation x2+10x=−25x^{2} + 10 x = −25

ⓐ by using the Square Root Property

ⓑ by Completing the Square

ⓒ Which method do you prefer? Why?

2.5

Adapted from Intermediate Algebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Intermediate Algebra 2e. Imported at revision 77a933c.