Question

Solve the following quadratic equation for all values of xx in simplest form.
16, left parenthesis, x, squared, minus, 4, right parenthesis, plus, 5, equals, minus, 10
16(x
2
−4)+5=
−10

Answer 1

To solve the quadratic equation \( 16(x^2 - 4) + 5 = -10 \), we'll start by simplifying and solving the equation step by step.

1. **Distribute and simplify the equation:**
\[
16(x^2 - 4) + 5 = -10
\]
\[
16x^2 - 64 + 5 = -10
\]
\[
16x^2 - 59 = -10
\]

2. **Add 59 to both sides:**
\[
16x^2 - 59 + 59 = -10 + 59
\]
\[
16x^2 = 49
\]

3. **Divide both sides by 16:**
\[
x^2 = \frac{49}{16}
\]

4. **Take the square root of both sides:**
\[
x = \pm \sqrt{\frac{49}{16}}
\]
\[
x = \pm \frac{7}{4}
\]

Thus, the solutions to the equation are:
\[
x = \frac{7}{4} \quad \text{and} \quad x = -\frac{7}{4}
\]

In simplest form, the solutions are:
\[
\boxed{\frac{7}{4}} \quad \text{and} \quad \boxed{-\frac{7}{4}}
\]