Certainly! Let's solve the given quadratic equation step-by-step.
The equation given is:
[tex]\[ 2\left(x^2 - 6\right) - 8 = 2 \][/tex]
### Step 1: Simplify the equation
First, distribute the 2 into the parentheses:
[tex]\[ 2(x^2 - 6) - 8 = 2 \][/tex]
This simplifies to:
[tex]\[ 2x^2 - 12 - 8 = 2 \][/tex]
Combine the constants on the left side:
[tex]\[ 2x^2 - 20 = 2 \][/tex]
### Step 2: Move all terms to one side
Subtract 2 from both sides to set the equation to 0:
[tex]\[ 2x^2 - 20 - 2 = 0 \][/tex]
This simplifies to:
[tex]\[ 2x^2 - 22 = 0 \][/tex]
### Step 3: Isolate the [tex]\(x^2\)[/tex] term
Add 22 to both sides to isolate the quadratic term:
[tex]\[ 2x^2 = 22 \][/tex]
Divide both sides by 2:
[tex]\[ x^2 = 11 \][/tex]
### Step 4: Solve for [tex]\(x\)[/tex]
To find [tex]\(x\)[/tex], take the square root of both sides of the equation:
[tex]\[ x = \pm \sqrt{11} \][/tex]
So, the solutions to the equation are:
[tex]\[ x = -\sqrt{11} \quad \text{and} \quad x = \sqrt{11} \][/tex]
Hence, the values of [tex]\(x\)[/tex] are:
[tex]\[ \boxed{-\sqrt{11}, \sqrt{11}} \][/tex]
