help help help!!

Question

Solve each of the quadratic equation below by factoring. be sure to state your solution(s) after you factor.

a) x^2 - 3x - 28 = 0

b) 3x^2 + 13x - 10 = 0

c) 3x^2 + 3x - 36 = 0

d) 9x^2 - 49 = 0

e) 8x2 + 5 = 14x

Thanks.

Answer 1

a) The equation x² - 3x - 28 = 0

Solve the equation by factoring.

Multiply first term x² and last term -28 = -28x²

The correct pair of the terms -7x and 4x multiply to -28x² and add to -3x.

Replace the middle term -3x with  -7x + 4x.

 x² - 7x + 4x - 28 = 0

Group the terms into two pairs.

 (x² - 7x) + (4x - 28) = 0

Factor out x from the first group  and factor out 4 from the second group.

 x(x - 7) + 4(x - 7)

Factor out common term x - 7.

 (x - 7)(x + 4) = 0

Apply zero product property.

x - 7 = 0 and x + 4 = 0

x = 7 and x = - 4

Solutions are x = 7 , -4.

Answer 2

b) The equation 3x² - 13x - 10 = 0

Solve the equation by factoring.

Multiply first term 3x² and last term -10 = -30x²

The correct pair of the terms -15x and +2x multiply to -30x² and add to -13x.

Replace the middle term -13x with  -15x +2x.

3x² - 15x + 2x - 10 = 0

Group the terms into two pairs.

 (3x² - 15x) + (2x - 10) = 0

Factor out x from the first group  and factor out 4 from the second group.

 3x(x - 5) + 2(x - 5)

Factor out common term x - 5.

 (x - 5)(3x + 2) = 0

Apply zero product property.

x - 5 = 0 and 3x + 2 = 0

x = 5 and x = - 2/3

Solutions are x = 5 , -2/3.

Answer 3

c) The equation 3x² + 3x - 36 = 0

Solve the equation by factoring.

Multiply first term 3x² and last term -36 = -108x²

The correct pair of the terms +12x and -9x multiply to -108x² and add to 3x.

Replace the middle term 3x with  12x -9x.

3x²  + 12x - 9x - 36 = 0

Group the terms into two pairs.

 (3x² + 12x) + (-9x - 36) = 0

Factor out x from the first group  and factor out 4 from the second group.

 3x(x + 4) - 9(x + 4)

Factor out common term x + 4.

 (x + 4)(3x - 9) = 0

Apply zero product property.

x + 4 = 0 and 3x - 9 = 0

x = -4 and x =  9/3

Solutions are x = -4 , 3.

Answer 4

d) The equation 9x² - 49 = 0

(3x)² - 7² = 0

Apply the formula a² - b² = (a - b)(a + b)

a = 3x, b = 7

(3x - 7)(3x + 7) = 0

Apply zero product property.

3x - 7 = 0 and 3x + 7 = 0

3x = 7 and 3x = - 7

Solutions are x = 7/3 and x = -7/3.

Answer 5

e) The equation 8x² + 5 = 14x

8x² - 14x + 5 = 0

Solve the equation by factoring.

Multiply first term 8x² and last term 5 = 40x²

The correct pair of the terms -10x and -4x multiply to 40x² and add to -14x.

Replace the middle term - 14x with  - 10x - 4x.

8x² - 10x - 4x + 5 = 0

Group the terms into two pairs.

 (8x² - 10x) + (- 4x + 5) = 0

Factor out x from the first group  and factor out 4 from the second group.

 2x(4x - 5) - 1(4x - 5)

Factor out common term 4x - 5.

 (4x - 5)(2x - 1) = 0

Apply zero product property.

4x - 5 = 0 and 2x - 1 = 0

4x = 5 and 2x = 1

x = 5/4 and x = 1/2

Solutions are x = 5/4 , 1/2.