Solve the following quadratic equation for all values of xx in simplest form.

Question

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:

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