Question

exercises within reach®
solving a quadratic equation by factoring
in exercises 27–44, solve the equation by factoring.

1. $4x^{2}+15x=25$
2. $-14x^{2}+9x=-1$
3. $7 + 13x - 2x^{2}=0$
4. $11 + 32y - 3y^{2}=0$
5. $3y^{2}-2=-y$
6. $-2x - 15=-x^{2}$
7. $21x - 36=3x^{2}$
8. $8x^{2}=-32x + 40$
9. $m^{2}-8m + 18=2$
10. $u^{2}+4u + 10=6$
11. $9x^{2}=25$
12. $-49x^{2}=-4$
13. $4 - 36x^{2}=0$
14. $0=50x^{2}-128$
15. $x^{2}+16x + 37=-7$
16. $x^{2}-12x + 21=-15$
17. $4z^{2}-12z + 15=6$
18. $16x^{2}+48x + 40=4$

Explanation:

Problem 27

Step1: Rearrange to standard form

$4x^2 + 15x - 25 = 0$

Step2: Factor the quadratic

$(4x - 5)(x + 5) = 0$

Step3: Solve for x

Set each factor to 0:
$4x - 5 = 0 \implies x = \frac{5}{4}$
$x + 5 = 0 \implies x = -5$

Step1: Rearrange to standard form

$-14x^2 + 9x + 1 = 0 \implies 14x^2 - 9x - 1 = 0$

Step2: Factor the quadratic

$(14x + 1)(x - 1) = 0$

Step3: Solve for x

Set each factor to 0:
$14x + 1 = 0 \implies x = -\frac{1}{14}$
$x - 1 = 0 \implies x = 1$

Step1: Rearrange to standard form

$-2x^2 + 13x + 7 = 0 \implies 2x^2 - 13x - 7 = 0$

Step2: Factor the quadratic

$(2x + 1)(x - 7) = 0$

Step3: Solve for x

Set each factor to 0:
$2x + 1 = 0 \implies x = -\frac{1}{2}$
$x - 7 = 0 \implies x = 7$

Answer:

$x = \frac{5}{4}, x = -5$

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Problem 28