Solve x^2+36x-86*18=0

$$x ^ { 2 } + 36 x - 86 \times 18 = 0$$

Solve for x

$$x=12\sqrt{13}-18\approx 25.266615306$$

$$x=-12\sqrt{13}-18\approx -61.266615306$$

Steps Using the Quadratic Formula

Multiply 86 and 18 to get 1548.

$$x^{2}+36x-1548=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 36 for b, and -1548 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-36±\sqrt{36^{2}-4\left(-1548\right)}}{2}$$

Square 36.

$$x=\frac{-36±\sqrt{1296-4\left(-1548\right)}}{2}$$

Multiply -4 times -1548.

$$x=\frac{-36±\sqrt{1296+6192}}{2}$$

Add 1296 to 6192.

$$x=\frac{-36±\sqrt{7488}}{2}$$

Take the square root of 7488.

$$x=\frac{-36±24\sqrt{13}}{2}$$

Now solve the equation x=\frac{-36±24\sqrt{13}}{2} when ± is plus. Add -36 to 24\sqrt{13}.

$$x=\frac{24\sqrt{13}-36}{2}$$

Divide -36+24\sqrt{13} by 2.

$$x=12\sqrt{13}-18$$

Now solve the equation x=\frac{-36±24\sqrt{13}}{2} when ± is minus. Subtract 24\sqrt{13} from -36.

$$x=\frac{-24\sqrt{13}-36}{2}$$

Divide -36-24\sqrt{13} by 2.

$$x=-12\sqrt{13}-18$$

The equation is now solved.

$$x=12\sqrt{13}-18 x=-12\sqrt{13}-18$$

Steps for Completing the Square

Multiply 86 and 18 to get 1548.

$$x^{2}+36x-1548=0$$

Add 1548 to both sides. Anything plus zero gives itself.

$$x^{2}+36x=1548$$

Divide 36, the coefficient of the x term, by 2 to get 18. Then add the square of 18 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+36x+18^{2}=1548+18^{2}$$

Square 18.

$$x^{2}+36x+324=1548+324$$

Add 1548 to 324.

$$x^{2}+36x+324=1872$$

Factor x^{2}+36x+324. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+18\right)^{2}=1872$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+18\right)^{2}}=\sqrt{1872}$$

Simplify.

$$x+18=12\sqrt{13} x+18=-12\sqrt{13}$$

Subtract 18 from both sides of the equation.

$$x=12\sqrt{13}-18 x=-12\sqrt{13}-18$$