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

Question

4, left parenthesis, x, squared, minus, 6, right parenthesis, minus, 3, equals, 9
4(x
2
−6)−3=
9

Answer 1

To solve the quadratic equation \(4(x^2 - 6) - 3 = 9\), we will first simplify and solve for \(x\).

1. Start with the given equation: \[ 4(x^2 - 6) - 3 = 9 \]

2. Add 3 to both sides: \[ 4(x^2 - 6) = 12 \]

3. Divide both sides by 4: \[ x^2 - 6 = 3 \]

4. Add 6 to both sides: \[ x^2 = 9 \]

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

Thus, the solutions to the equation are: \[ x = 3 \quad \text{and} \quad x = -3 \]

These are the solutions in simplest form.