Solve 80=x*(x-8)

$$80 = x \cdot ( x - 8 )$$

Solve for x

$$x=4\sqrt{6}+4\approx 13.797958971$$

$$x=4-4\sqrt{6}\approx -5.797958971$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x-8.

$$80=x^{2}-8x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-8x=80$$

Subtract 80 from both sides.

$$x^{2}-8x-80=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -8 for b, and -80 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-80\right)}}{2}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-80\right)}}{2}$$

Multiply -4 times -80.

$$x=\frac{-\left(-8\right)±\sqrt{64+320}}{2}$$

Add 64 to 320.

$$x=\frac{-\left(-8\right)±\sqrt{384}}{2}$$

Take the square root of 384.

$$x=\frac{-\left(-8\right)±8\sqrt{6}}{2}$$

The opposite of -8 is 8.

$$x=\frac{8±8\sqrt{6}}{2}$$

Now solve the equation x=\frac{8±8\sqrt{6}}{2} when ± is plus. Add 8 to 8\sqrt{6}.

$$x=\frac{8\sqrt{6}+8}{2}$$

Divide 8+8\sqrt{6} by 2.

$$x=4\sqrt{6}+4$$

Now solve the equation x=\frac{8±8\sqrt{6}}{2} when ± is minus. Subtract 8\sqrt{6} from 8.

$$x=\frac{8-8\sqrt{6}}{2}$$

Divide 8-8\sqrt{6} by 2.

$$x=4-4\sqrt{6}$$

The equation is now solved.

$$x=4\sqrt{6}+4 x=4-4\sqrt{6}$$

Steps for Completing the Square

Use the distributive property to multiply x by x-8.

$$80=x^{2}-8x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-8x=80$$

Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-8x+\left(-4\right)^{2}=80+\left(-4\right)^{2}$$

Square -4.

$$x^{2}-8x+16=80+16$$

Add 80 to 16.

$$x^{2}-8x+16=96$$

Factor x^{2}-8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-4\right)^{2}=96$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{96}$$

Simplify.

$$x-4=4\sqrt{6} x-4=-4\sqrt{6}$$

Add 4 to both sides of the equation.

$$x=4\sqrt{6}+4 x=4-4\sqrt{6}$$