Question

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

Answer 1

To solve the quadratic equation \( 3(x^2 - 7) + 4 = 4 \), we can follow these steps:

1. **Simplify the equation**:
\[
3(x^2 - 7) + 4 = 4
\]
Subtract 4 from both sides:
\[
3(x^2 - 7) = 0
\]

2. **Divide by 3**:
\[
x^2 - 7 = 0
\]

3. **Solve for \( x^2 \)**:
\[
x^2 = 7
\]

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

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

These are the values of \( x \) in simplest form.