Question

Solve the following quadratic equation for all values of xx in simplest form.
4, left parenthesis, x, squared, minus, 7, right parenthesis, minus, 10, equals, minus, 13
4(x
2
−7)−10=
−13

Answer 1

To solve the given quadratic equation:

\[ 4(x^2 - 7) - 10 = -13 \]

Let's simplify and solve step by step.

1. Distribute the 4 in the equation:

\[
4x^2 - 28 - 10 = -13
\]

2. Combine like terms:

\[
4x^2 - 38 = -13
\]

3. Add 38 to both sides to isolate the \(4x^2\):

\[
4x^2 = -13 + 38
\]

\[
4x^2 = 25
\]

4. Divide both sides by 4:

\[
x^2 = \frac{25}{4}
\]

5. Take the square root of both sides:

\[
x = \pm \sqrt{\frac{25}{4}}
\]

\[
x = \pm \frac{5}{2}
\]

Thus, the solutions for \(x\) are:

\[
x = \frac{5}{2} \quad \text{and} \quad x = -\frac{5}{2}
\]

In simplest form, the solutions are:

\[
x = \frac{5}{2}, \, -\frac{5}{2}
\]