Solve x^2-18x=-2x+64

$$x ^ { 2 } - 18 x = - 2 x + 64$$

Solve for x

$$x=8\sqrt{2}+8\approx 19.313708499$$

$$x=8-8\sqrt{2}\approx -3.313708499$$

Steps Using the Quadratic Formula

Add 2x to both sides.

$$x^{2}-18x+2x=64$$

Combine -18x and 2x to get -16x.

$$x^{2}-16x=64$$

Subtract 64 from both sides.

$$x^{2}-16x-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -16 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-64\right)}}{2}$$

Square -16.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-64\right)}}{2}$$

Multiply -4 times -64.

$$x=\frac{-\left(-16\right)±\sqrt{256+256}}{2}$$

Add 256 to 256.

$$x=\frac{-\left(-16\right)±\sqrt{512}}{2}$$

Take the square root of 512.

$$x=\frac{-\left(-16\right)±16\sqrt{2}}{2}$$

The opposite of -16 is 16.

$$x=\frac{16±16\sqrt{2}}{2}$$

Now solve the equation x=\frac{16±16\sqrt{2}}{2} when ± is plus. Add 16 to 16\sqrt{2}.

$$x=\frac{16\sqrt{2}+16}{2}$$

Divide 16+16\sqrt{2} by 2.

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

Now solve the equation x=\frac{16±16\sqrt{2}}{2} when ± is minus. Subtract 16\sqrt{2} from 16.

$$x=\frac{16-16\sqrt{2}}{2}$$

Divide 16-16\sqrt{2} by 2.

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

The equation is now solved.

$$x=8\sqrt{2}+8 x=8-8\sqrt{2}$$

Steps for Completing the Square

Add 2x to both sides.

$$x^{2}-18x+2x=64$$

Combine -18x and 2x to get -16x.

$$x^{2}-16x=64$$

Divide -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-16x+\left(-8\right)^{2}=64+\left(-8\right)^{2}$$

Square -8.

$$x^{2}-16x+64=64+64$$

Add 64 to 64.

$$x^{2}-16x+64=128$$

Factor x^{2}-16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-8\right)^{2}=128$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{128}$$

Simplify.

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

Add 8 to both sides of the equation.

$$x=8\sqrt{2}+8 x=8-8\sqrt{2}$$