Find the Roots (Zeros) g(x)=2(x-3)^2-8

$g (x) = 2 {(x - 3)}^{2} - 8$

Step 1

Set $2 {(x - 3)}^{2} - 8$ equal to $0$ .

$2 {(x - 3)}^{2} - 8 = 0$

Step 2

Solve for $x$ .

Simplify $2 {(x - 3)}^{2} - 8$ .

Simplify each term.

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$2 ((x - 3) (x - 3)) - 8 = 0$

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$2 (x (x - 3) - 3 (x - 3)) - 8 = 0$

Apply the distributive property.

$2 (x \cdot x + x \cdot - 3 - 3 (x - 3)) - 8 = 0$

Apply the distributive property.

$2 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3) - 8 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$2 (x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3) - 8 = 0$

Move $- 3$ to the left of $x$ .

$2 (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3) - 8 = 0$

Multiply $- 3$ by $- 3$ .

$2 (x^{2} - 3 x - 3 x + 9) - 8 = 0$

Subtract $3 x$ from $- 3 x$ .

$2 (x^{2} - 6 x + 9) - 8 = 0$

Apply the distributive property.

$2 x^{2} + 2 (- 6 x) + 2 \cdot 9 - 8 = 0$

Simplify.

Multiply $- 6$ by $2$ .

$2 x^{2} - 12 x + 2 \cdot 9 - 8 = 0$

Multiply $2$ by $9$ .

$2 x^{2} - 12 x + 18 - 8 = 0$

Subtract $8$ from $18$ .

$2 x^{2} - 12 x + 10 = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 1, 5$

Step 3