Solve left(x-4right)(x+4)*2=8-4(10-x)

$$\left( x-4 \right) (x+4) \times 2=8-4(10-x)$$

Solve for x

$$x=2$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-4 by x+4 and combine like terms.

$$\left(x^{2}-16\right)\times 2=8-4\left(10-x\right)$$

Use the distributive property to multiply x^{2}-16 by 2.

$$2x^{2}-32=8-4\left(10-x\right)$$

Use the distributive property to multiply -4 by 10-x.

$$2x^{2}-32=8-40+4x$$

Subtract 40 from 8 to get -32.

$$2x^{2}-32=-32+4x$$

Subtract -32 from both sides.

$$2x^{2}-32-\left(-32\right)=4x$$

The opposite of -32 is 32.

$$2x^{2}-32+32=4x$$

Subtract 4x from both sides.

$$2x^{2}-32+32-4x=0$$

Add -32 and 32 to get 0.

$$2x^{2}-4x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -4 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2\times 2}$$

Take the square root of \left(-4\right)^{2}.

$$x=\frac{-\left(-4\right)±4}{2\times 2}$$

The opposite of -4 is 4.

$$x=\frac{4±4}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{4±4}{4}$$

Now solve the equation x=\frac{4±4}{4} when ± is plus. Add 4 to 4.

$$x=\frac{8}{4}$$

Divide 8 by 4.

$$x=2$$

Now solve the equation x=\frac{4±4}{4} when ± is minus. Subtract 4 from 4.

$$x=\frac{0}{4}$$

Divide 0 by 4.

$$x=0$$

The equation is now solved.

$$x=2 x=0$$

Steps for Completing the Square

Use the distributive property to multiply x-4 by x+4 and combine like terms.

$$\left(x^{2}-16\right)\times 2=8-4\left(10-x\right)$$

Use the distributive property to multiply x^{2}-16 by 2.

$$2x^{2}-32=8-4\left(10-x\right)$$

Use the distributive property to multiply -4 by 10-x.

$$2x^{2}-32=8-40+4x$$

Subtract 40 from 8 to get -32.

$$2x^{2}-32=-32+4x$$

Subtract 4x from both sides.

$$2x^{2}-32-4x=-32$$

Add 32 to both sides.

$$2x^{2}-4x=-32+32$$

Add -32 and 32 to get 0.

$$2x^{2}-4x=0$$

Divide both sides by 2.

$$\frac{2x^{2}-4x}{2}=\frac{0}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{4}{2}\right)x=\frac{0}{2}$$

Divide -4 by 2.

$$x^{2}-2x=\frac{0}{2}$$

Divide 0 by 2.

$$x^{2}-2x=0$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-2x+1=1$$

Factor x^{2}-2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$x-1=1 x-1=-1$$

Add 1 to both sides of the equation.

$$x=2 x=0$$