Solve 0=x^2-286x-288

$$0 = x ^ { 2 } - 286 x - 288$$

Solve for x

$$x=\sqrt{20737}+143\approx 287.00347218$$

$$x=143-\sqrt{20737}\approx -1.00347218$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-286x-288=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -286 for b, and -288 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-286\right)±\sqrt{\left(-286\right)^{2}-4\left(-288\right)}}{2}$$

Square -286.

$$x=\frac{-\left(-286\right)±\sqrt{81796-4\left(-288\right)}}{2}$$

Multiply -4 times -288.

$$x=\frac{-\left(-286\right)±\sqrt{81796+1152}}{2}$$

Add 81796 to 1152.

$$x=\frac{-\left(-286\right)±\sqrt{82948}}{2}$$

Take the square root of 82948.

$$x=\frac{-\left(-286\right)±2\sqrt{20737}}{2}$$

The opposite of -286 is 286.

$$x=\frac{286±2\sqrt{20737}}{2}$$

Now solve the equation x=\frac{286±2\sqrt{20737}}{2} when ± is plus. Add 286 to 2\sqrt{20737}.

$$x=\frac{2\sqrt{20737}+286}{2}$$

Divide 286+2\sqrt{20737} by 2.

$$x=\sqrt{20737}+143$$

Now solve the equation x=\frac{286±2\sqrt{20737}}{2} when ± is minus. Subtract 2\sqrt{20737} from 286.

$$x=\frac{286-2\sqrt{20737}}{2}$$

Divide 286-2\sqrt{20737} by 2.

$$x=143-\sqrt{20737}$$

The equation is now solved.

$$x=\sqrt{20737}+143 x=143-\sqrt{20737}$$

Steps for Completing the Square

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-286x-288=0$$

Add 288 to both sides. Anything plus zero gives itself.

$$x^{2}-286x=288$$

Divide -286, the coefficient of the x term, by 2 to get -143. Then add the square of -143 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-286x+\left(-143\right)^{2}=288+\left(-143\right)^{2}$$

Square -143.

$$x^{2}-286x+20449=288+20449$$

Add 288 to 20449.

$$x^{2}-286x+20449=20737$$

Factor x^{2}-286x+20449. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-143\right)^{2}=20737$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-143\right)^{2}}=\sqrt{20737}$$

Simplify.

$$x-143=\sqrt{20737} x-143=-\sqrt{20737}$$

Add 143 to both sides of the equation.

$$x=\sqrt{20737}+143 x=143-\sqrt{20737}$$