Solve 8x^2+18x-8=636*2

$$8 { x }^{ 2 } +18x-8=636 \times 2$$

Solve for x

$$x = \frac{\sqrt{10321} - 9}{8} \approx 11.574040318$$

$$x=\frac{-\sqrt{10321}-9}{8}\approx -13.824040318$$

Steps Using the Quadratic Formula

Multiply 636 and 2 to get 1272.

$$8x^{2}+18x-8=1272$$

Subtract 1272 from both sides.

$$8x^{2}+18x-8-1272=0$$

Subtract 1272 from -8 to get -1280.

$$8x^{2}+18x-1280=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 18 for b, and -1280 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\times 8\left(-1280\right)}}{2\times 8}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\times 8\left(-1280\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-18±\sqrt{324-32\left(-1280\right)}}{2\times 8}$$

Multiply -32 times -1280.

$$x=\frac{-18±\sqrt{324+40960}}{2\times 8}$$

Add 324 to 40960.

$$x=\frac{-18±\sqrt{41284}}{2\times 8}$$

Take the square root of 41284.

$$x=\frac{-18±2\sqrt{10321}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-18±2\sqrt{10321}}{16}$$

Now solve the equation x=\frac{-18±2\sqrt{10321}}{16} when ± is plus. Add -18 to 2\sqrt{10321}.

$$x=\frac{2\sqrt{10321}-18}{16}$$

Divide -18+2\sqrt{10321} by 16.

$$x=\frac{\sqrt{10321}-9}{8}$$

Now solve the equation x=\frac{-18±2\sqrt{10321}}{16} when ± is minus. Subtract 2\sqrt{10321} from -18.

$$x=\frac{-2\sqrt{10321}-18}{16}$$

Divide -18-2\sqrt{10321} by 16.

$$x=\frac{-\sqrt{10321}-9}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{10321}-9}{8} x=\frac{-\sqrt{10321}-9}{8}$$

Steps for Completing the Square

Multiply 636 and 2 to get 1272.

$$8x^{2}+18x-8=1272$$

Add 8 to both sides.

$$8x^{2}+18x=1272+8$$

Add 1272 and 8 to get 1280.

$$8x^{2}+18x=1280$$

Divide both sides by 8.

$$\frac{8x^{2}+18x}{8}=\frac{1280}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x^{2}+\frac{18}{8}x=\frac{1280}{8}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$x^{2}+\frac{9}{4}x=\frac{1280}{8}$$

Divide 1280 by 8.

$$x^{2}+\frac{9}{4}x=160$$

Divide \frac{9}{4}, the coefficient of the x term, by 2 to get \frac{9}{8}. Then add the square of \frac{9}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{9}{4}x+\left(\frac{9}{8}\right)^{2}=160+\left(\frac{9}{8}\right)^{2}$$

Square \frac{9}{8} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{9}{4}x+\frac{81}{64}=160+\frac{81}{64}$$

Add 160 to \frac{81}{64}.

$$x^{2}+\frac{9}{4}x+\frac{81}{64}=\frac{10321}{64}$$

Factor x^{2}+\frac{9}{4}x+\frac{81}{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}.

$$\left(x+\frac{9}{8}\right)^{2}=\frac{10321}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{9}{8}\right)^{2}}=\sqrt{\frac{10321}{64}}$$

Simplify.

$$x+\frac{9}{8}=\frac{\sqrt{10321}}{8} x+\frac{9}{8}=-\frac{\sqrt{10321}}{8}$$

Subtract \frac{9}{8} from both sides of the equation.

$$x=\frac{\sqrt{10321}-9}{8} x=\frac{-\sqrt{10321}-9}{8}$$