Question

Solve for x. write both solutions, separated by a comma. 3x%20-%209%20%3D%200" id="TexFormula1" title=" {2x}^{2} + 3x - 9 = 0" alt=" {2x}^{2} + 3x - 9 = 0" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

x = -3 and x = 3/2

Step-by-step explanation:

2x^2 + 3x - 9 = 0

2x^2 + 6x - 3x - 9 =0

2x(x + 3) - 3(x + 3) = 0

(2x - 3)(x + 3) = 0

2x - 3 = 0; x = 3/2

x + 3 = 0; x = -3

Answer 2

Answer:

see explanation

Step-by-step explanation:

given

2x² + 3x - 9 = 0

To factor

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 9 = - 18 and sum = + 3

The factors are + 6 and - 3

Use these factors to split the x- term

2x² + 6x - 3x - 9 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 3(x + 3) = 0 ← factor out (x + 3)

(x + 3)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = $\frac{3}{2}$

Solutions are x = - 3, $\frac{3}{2}$