II. Find the solution set of the following quadratic equations by factoring:

x^2 - 8x - 9 = 0

100x^2 - 20x = 0

2x^2 - 7x - 15 = 0

x^2 +9x +13 = - 5x-20

3x^2 - 12x + 5 = 9 - 4x^2

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Step-by-step explanation:

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see explanation

Step-by-step explanation:

x² - 8x - 9 = 0 ← in standard form

(x - 9)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 1 = 0 ⇒ x = - 1

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100x² - 20x = 0 ( divide through by 20 )

5x² - x = 0 ( factor out x from each term )

x(5x - 1) = 0

x = 0

5x - 1 = 0 ⇒ 5x = 1 ⇒ x =

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2x² - 7x - 15 = 0 ← in standard form

(2x + 3)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -

x - 5 = 0 ⇒ x = 5

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x² + 9x + 13 = - 5x - 20 (add 5x + 20 to both sides )

x² + 14x + 33 = 0 ← in standard form

(x + 11)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 11 = 0 ⇒ x = - 11

x + 3 = 0 ⇒ x = - 3

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3x² - 12x + 5 = 9 - 4x² ( subtract 9 - 4x² from both sides )

7x² - 12x - 4 = 0 ← in standard form

(7x + 2)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

7x + 2 = 0 ⇒ 7x = - 2 ⇒ x = -

x - 2 = 0 ⇒ x = 2

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step-by-step explanation: