Solve (x-9)^2=81

$$( x - 9 ) ^ { 2 } = 81$$

Solve for x

$$x=18$$

$$x=0$$

Steps Using Factoring

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-9\right)^{2}.

$$x^{2}-18x+81=81$$

Subtract 81 from both sides.

$$x^{2}-18x+81-81=0$$

Subtract 81 from 81 to get 0.

$$x^{2}-18x=0$$

Factor out x.

$$x\left(x-18\right)=0$$

To find equation solutions, solve x=0 and x-18=0.

$$x=0 x=18$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-9\right)^{2}.

$$x^{2}-18x+81=81$$

Subtract 81 from both sides.

$$x^{2}-18x+81-81=0$$

Subtract 81 from 81 to get 0.

$$x^{2}-18x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -18 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2}$$

Take the square root of \left(-18\right)^{2}.

$$x=\frac{-\left(-18\right)±18}{2}$$

The opposite of -18 is 18.

$$x=\frac{18±18}{2}$$

Now solve the equation x=\frac{18±18}{2} when ± is plus. Add 18 to 18.

$$x=\frac{36}{2}$$

Divide 36 by 2.

$$x=18$$

Now solve the equation x=\frac{18±18}{2} when ± is minus. Subtract 18 from 18.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=18 x=0$$

Steps for Completing the Square

Take the square root of both sides of the equation.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{81}$$

Simplify.

$$x-9=9 x-9=-9$$

Add 9 to both sides of the equation.

$$x=18 x=0$$