Solve for x 4(x-2)^2+320=0

$4 {(x - 2)}^{2} + 320 = 0$

Step 1

Simplify $4 {(x - 2)}^{2} + 320$ .

Simplify each term.

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

$4 ((x - 2) (x - 2)) + 320 = 0$

Expand $(x - 2) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$4 (x (x - 2) - 2 (x - 2)) + 320 = 0$

Apply the distributive property.

$4 (x \cdot x + x \cdot - 2 - 2 (x - 2)) + 320 = 0$

Apply the distributive property.

$4 (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2) + 320 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$4 (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2) + 320 = 0$

Move $- 2$ to the left of $x$ .

$4 (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2) + 320 = 0$

Multiply $- 2$ by $- 2$ .

$4 (x^{2} - 2 x - 2 x + 4) + 320 = 0$

Subtract $2 x$ from $- 2 x$ .

$4 (x^{2} - 4 x + 4) + 320 = 0$

Apply the distributive property.

$4 x^{2} + 4 (- 4 x) + 4 \cdot 4 + 320 = 0$

Simplify.

Multiply $- 4$ by $4$ .

$4 x^{2} - 16 x + 4 \cdot 4 + 320 = 0$

Multiply $4$ by $4$ .

$4 x^{2} - 16 x + 16 + 320 = 0$

Add $16$ and $320$ .

$4 x^{2} - 16 x + 336 = 0$

Step 2

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

No solution