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

Question

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.