Questions: Solve by factoring: 2x^2 + 3x = 2 a. 1/2, -2 b. 1/2, 2 c. -1/2, 2 d. -1/2, -2

Solve by factoring: 2x^2 + 3x = 2 a. 1/2, -2 b. 1/2, 2 c. -1/2, 2 d. -1/2, -2
Transcript text: Solve by factoring: $2 x^{2}+3 x=2$ a. $\frac{1}{2},-2$ b. $\frac{1}{2}, 2$ c. $-\frac{1}{2}, 2$ d. $-\frac{1}{2},-2$
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Solution

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Solution Steps

To solve the quadratic equation \(2x^2 + 3x = 2\) by factoring, follow these steps:

  1. Move all terms to one side of the equation to set it to zero: \(2x^2 + 3x - 2 = 0\).
  2. Factor the quadratic equation.
  3. Solve for the values of \(x\) by setting each factor equal to zero.
Step 1: Move All Terms to One Side

To solve the quadratic equation \(2x^2 + 3x = 2\) by factoring, we first move all terms to one side to set the equation to zero: \[ 2x^2 + 3x - 2 = 0 \]

Step 2: Factor the Quadratic Equation

Next, we factor the quadratic equation: \[ 2x^2 + 3x - 2 = (x + 2)(2x - 1) \]

Step 3: Solve for \(x\)

We solve for \(x\) by setting each factor equal to zero: \[ x + 2 = 0 \quad \text{or} \quad 2x - 1 = 0 \] Solving these equations, we get: \[ x = -2 \quad \text{or} \quad x = \frac{1}{2} \]

Final Answer

The solutions to the equation \(2x^2 + 3x - 2 = 0\) are: \[ \boxed{x = -2 \quad \text{and} \quad x = \frac{1}{2}} \]

For the multiple-choice question, the correct answer is: \[ \boxed{\text{a. } \frac{1}{2}, -2} \]

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