Solve 2x(4-x)=8x-4

$$2x(4-x)=8x-4$$

Solve for x

$$x=\sqrt{2}\approx 1.414213562$$

$$x=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Use the distributive property to multiply 2x by 4-x.

$$8x-2x^{2}=8x-4$$

Subtract 8x from both sides.

$$8x-2x^{2}-8x=-4$$

Combine 8x and -8x to get 0.

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

Divide both sides by -2.

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

Divide -4 by -2 to get 2.

$$x^{2}=2$$

Take the square root of both sides of the equation.

$$x=\sqrt{2} x=-\sqrt{2}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x by 4-x.

$$8x-2x^{2}=8x-4$$

Subtract 8x from both sides.

$$8x-2x^{2}-8x=-4$$

Combine 8x and -8x to get 0.

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

Add 4 to both sides.

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

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

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

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 4}}{2\left(-2\right)}$$

Multiply 8 times 4.

$$x=\frac{0±\sqrt{32}}{2\left(-2\right)}$$

Take the square root of 32.

$$x=\frac{0±4\sqrt{2}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{2}}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{-4} when ± is plus.

$$x=-\sqrt{2}$$

Now solve the equation x=\frac{0±4\sqrt{2}}{-4} when ± is minus.

$$x=\sqrt{2}$$

The equation is now solved.

$$x=-\sqrt{2} x=\sqrt{2}$$