Solve x^2+18x+81=-18+81

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

Solve for x

$$x=3\sqrt{7}-9\approx -1.062746067$$

$$x=-3\sqrt{7}-9\approx -16.937253933$$

Steps Using the Quadratic Formula

Add -18 and 81 to get 63.

$$x^{2}+18x+81=63$$

Subtract 63 from both sides.

$$x^{2}+18x+81-63=0$$

Subtract 63 from 81 to get 18.

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

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

$$x=\frac{-18±\sqrt{18^{2}-4\times 18}}{2}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\times 18}}{2}$$

Multiply -4 times 18.

$$x=\frac{-18±\sqrt{324-72}}{2}$$

Add 324 to -72.

$$x=\frac{-18±\sqrt{252}}{2}$$

Take the square root of 252.

$$x=\frac{-18±6\sqrt{7}}{2}$$

Now solve the equation x=\frac{-18±6\sqrt{7}}{2} when ± is plus. Add -18 to 6\sqrt{7}.

$$x=\frac{6\sqrt{7}-18}{2}$$

Divide -18+6\sqrt{7} by 2.

$$x=3\sqrt{7}-9$$

Now solve the equation x=\frac{-18±6\sqrt{7}}{2} when ± is minus. Subtract 6\sqrt{7} from -18.

$$x=\frac{-6\sqrt{7}-18}{2}$$

Divide -18-6\sqrt{7} by 2.

$$x=-3\sqrt{7}-9$$

The equation is now solved.

$$x=3\sqrt{7}-9 x=-3\sqrt{7}-9$$

Steps for Completing the Square

Add -18 to 81.

$$x^{2}+18x+81=63$$

Factor x^{2}+18x+81. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+9\right)^{2}=63$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{63}$$

Simplify.

$$x+9=3\sqrt{7} x+9=-3\sqrt{7}$$

Subtract 9 from both sides of the equation.

$$x=3\sqrt{7}-9 x=-3\sqrt{7}-9$$