Questions: Solve the equation by factoring. 14 x^2 + 3 x - 2 = 0 Rewrite the equation in factored form. (7 x - 2)(2 x + 1) = 0 (Factor completely.) The solution set is (Use a comma to separate answers as needed. Type each solution)

Solve the equation by factoring. 14 x^2 + 3 x - 2 = 0 Rewrite the equation in factored form. (7 x - 2)(2 x + 1) = 0 (Factor completely.) The solution set is (Use a comma to separate answers as needed. Type each solution)
Transcript text: Solve the equation by factoring. \[ 14 x^{2}+3 x-2=0 \] Rewrite the equation in factored form. \[ (7 x-2)(2 x+1)=0 \] (Factor completely.) The solution set is $\square$ (Use a comma to separate answers as needed. Type each solution o
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Solution

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To solve the quadratic equation by factoring, we first rewrite the equation in its factored form. Then, we set each factor equal to zero and solve for \( x \).

Paso 1: Reescribir la ecuación en forma factorizada

Dada la ecuación cuadrática: \[ 14x^2 + 3x - 2 = 0 \] La forma factorizada de la ecuación es: \[ (7x - 2)(2x + 1) = 0 \]

Paso 2: Resolver cada factor por separado

Para encontrar las soluciones, igualamos cada factor a cero y resolvemos para \( x \).

  1. \( 7x - 2 = 0 \) \[ 7x = 2 \implies x = \frac{2}{7} \]

  2. \( 2x + 1 = 0 \) \[ 2x = -1 \implies x = -\frac{1}{2} \]

Respuesta Final

El conjunto de soluciones es: \[ \boxed{\left\{ -\frac{1}{2}, \frac{2}{7} \right\}} \]

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