Question

Solve the following quadratic equation for all values of xx in simplest form.
5, left parenthesis, x, squared, minus, 7, right parenthesis, minus, 1, equals, 9
5(x
2
−7)−1=
9

Answer 1

To solve the quadratic equation \( 5(x^2 - 7) - 1 = 9 \), we can follow these steps:

1. Start by simplifying the equation:
\[
5(x^2 - 7) - 1 = 9
\]

2. Add 1 to both sides:
\[
5(x^2 - 7) = 10
\]

3. Divide both sides by 5:
\[
x^2 - 7 = 2
\]

4. Add 7 to both sides:
\[
x^2 = 9
\]

5. Now, take the square root of both sides:
\[
x = \pm 3
\]

Therefore, the solutions for the quadratic equation are:
\[
x = 3 \quad \text{and} \quad x = -3
\]