Pregunta
Solve the equation by factoring. \( 16 x^{2}+2 x-3=0 \) Rewrite the equation in factored form \( (8 x-3)(2 x+1)=0 \) (Factor completely.) The solution set is \( \} \) (Use a comma to separate answers as needed.
Ask by Wang Reid. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The solutions are \( x = -\frac{1}{2} \) and \( x = \frac{3}{8} \).
Solución
To solve the equation \( 16x^{2} + 2x - 3 = 0 \) by factoring, follow these steps:
1. **Factor the quadratic equation:**
The given equation can be factored as:
\[
(8x - 3)(2x + 1) = 0
\]
2. **Find the solutions by setting each factor equal to zero:**
- **First factor:**
\[
8x - 3 = 0 \\
8x = 3 \\
x = \frac{3}{8}
\]
- **Second factor:**
\[
2x + 1 = 0 \\
2x = -1 \\
x = -\frac{1}{2}
\]
3. **Write the solution set:**
The solutions to the equation are:
\[
\left\{ -\frac{1}{2}, \frac{3}{8} \right\}
\]
**Answer:**
\(\left\{\, -\dfrac{1}{2},\; \dfrac{3}{8} \,\right\}\)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
First, let's break down the factored form of the equation \( (8x - 3)(2x + 1) = 0 \). To find the solutions, we set each factor to zero. For the first factor, \( 8x - 3 = 0 \) gives \( 8x = 3 \) and then \( x = \frac{3}{8} \). For the second factor, \( 2x + 1 = 0 \) leads to \( 2x = -1 \) and thus \( x = -\frac{1}{2} \). Therefore, the solution set is \( \left\{ \frac{3}{8}, -\frac{1}{2} \right\} \). Now that we have the solution, be sure to double-check by substituting the values back into the original equation to confirm they work. It's always good to verify that the factored forms yield the same output when plugged back into the equation! Happy solving!
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