Solve x^2-0x^2+20x-2x-16=0

$$x ^ { 2 } - 0 x ^ { 2 } + 20 x - 2 x - 16 = 0$$

Solve for x (complex solution)

$$x=\sqrt{97}-9\approx 0.848857802$$

$$x=-\left(\sqrt{97}+9\right)\approx -18.848857802$$

Steps Using the Quadratic Formula

Anything times zero gives zero.

$$x^{2}-0+20x-2x-16=0$$

Combine 20x and -2x to get 18x.

$$x^{2}-0+18x-16=0$$

Reorder the terms.

$$x^{2}+18x-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 18 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-16\right)}}{2}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$x=\frac{-18±\sqrt{324+64}}{2}$$

Add 324 to 64.

$$x=\frac{-18±\sqrt{388}}{2}$$

Take the square root of 388.

$$x=\frac{-18±2\sqrt{97}}{2}$$

Now solve the equation x=\frac{-18±2\sqrt{97}}{2} when ± is plus. Add -18 to 2\sqrt{97}.

$$x=\frac{2\sqrt{97}-18}{2}$$

Divide -18+2\sqrt{97} by 2.

$$x=\sqrt{97}-9$$

Now solve the equation x=\frac{-18±2\sqrt{97}}{2} when ± is minus. Subtract 2\sqrt{97} from -18.

$$x=\frac{-2\sqrt{97}-18}{2}$$

Divide -18-2\sqrt{97} by 2.

$$x=-\sqrt{97}-9$$

The equation is now solved.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Steps for Completing the Square

Anything times zero gives zero.

$$x^{2}-0+20x-2x-16=0$$

Combine 20x and -2x to get 18x.

$$x^{2}-0+18x-16=0$$

Add 16 to both sides. Anything plus zero gives itself.

$$x^{2}-0+18x=16$$

Reorder the terms.

$$x^{2}+18x=16$$

Divide 18, the coefficient of the x term, by 2 to get 9. Then add the square of 9 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+18x+9^{2}=16+9^{2}$$

Square 9.

$$x^{2}+18x+81=16+81$$

Add 16 to 81.

$$x^{2}+18x+81=97$$

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}.

$$\left(x+9\right)^{2}=97$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{97}$$

Simplify.

$$x+9=\sqrt{97} x+9=-\sqrt{97}$$

Subtract 9 from both sides of the equation.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Solve for x

$$x=\sqrt{97}-9\approx 0.848857802$$

$$x=-\sqrt{97}-9\approx -18.848857802$$

Steps Using the Quadratic Formula

Anything times zero gives zero.

$$x^{2}-0+20x-2x-16=0$$

Combine 20x and -2x to get 18x.

$$x^{2}-0+18x-16=0$$

Reorder the terms.

$$x^{2}+18x-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 18 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-16\right)}}{2}$$

Square 18.

$$x=\frac{-18±\sqrt{324-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$x=\frac{-18±\sqrt{324+64}}{2}$$

Add 324 to 64.

$$x=\frac{-18±\sqrt{388}}{2}$$

Take the square root of 388.

$$x=\frac{-18±2\sqrt{97}}{2}$$

Now solve the equation x=\frac{-18±2\sqrt{97}}{2} when ± is plus. Add -18 to 2\sqrt{97}.

$$x=\frac{2\sqrt{97}-18}{2}$$

Divide -18+2\sqrt{97} by 2.

$$x=\sqrt{97}-9$$

Now solve the equation x=\frac{-18±2\sqrt{97}}{2} when ± is minus. Subtract 2\sqrt{97} from -18.

$$x=\frac{-2\sqrt{97}-18}{2}$$

Divide -18-2\sqrt{97} by 2.

$$x=-\sqrt{97}-9$$

The equation is now solved.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$

Steps for Completing the Square

Anything times zero gives zero.

$$x^{2}-0+20x-2x-16=0$$

Combine 20x and -2x to get 18x.

$$x^{2}-0+18x-16=0$$

Add 16 to both sides. Anything plus zero gives itself.

$$x^{2}-0+18x=16$$

Reorder the terms.

$$x^{2}+18x=16$$

Divide 18, the coefficient of the x term, by 2 to get 9. Then add the square of 9 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+18x+9^{2}=16+9^{2}$$

Square 9.

$$x^{2}+18x+81=16+81$$

Add 16 to 81.

$$x^{2}+18x+81=97$$

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}.

$$\left(x+9\right)^{2}=97$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{97}$$

Simplify.

$$x+9=\sqrt{97} x+9=-\sqrt{97}$$

Subtract 9 from both sides of the equation.

$$x=\sqrt{97}-9 x=-\sqrt{97}-9$$