Solve 0=x^2-60x+950

$$0 = x ^ { 2 } - 60 x + 950$$

Solve for x (complex solution)

$$x=30+5\sqrt{2}i\approx 30+7.071067812i$$

$$x=-5\sqrt{2}i+30\approx 30-7.071067812i$$

Steps Using the Quadratic Formula

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

$$x^{2}-60x+950=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -60 for b, and 950 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-60\right)±\sqrt{\left(-60\right)^{2}-4\times 950}}{2}$$

Square -60.

$$x=\frac{-\left(-60\right)±\sqrt{3600-4\times 950}}{2}$$

Multiply -4 times 950.

$$x=\frac{-\left(-60\right)±\sqrt{3600-3800}}{2}$$

Add 3600 to -3800.

$$x=\frac{-\left(-60\right)±\sqrt{-200}}{2}$$

Take the square root of -200.

$$x=\frac{-\left(-60\right)±10\sqrt{2}i}{2}$$

The opposite of -60 is 60.

$$x=\frac{60±10\sqrt{2}i}{2}$$

Now solve the equation x=\frac{60±10\sqrt{2}i}{2} when ± is plus. Add 60 to 10i\sqrt{2}.

$$x=\frac{60+10\sqrt{2}i}{2}$$

Divide 60+10i\sqrt{2} by 2.

$$x=30+5\sqrt{2}i$$

Now solve the equation x=\frac{60±10\sqrt{2}i}{2} when ± is minus. Subtract 10i\sqrt{2} from 60.

$$x=\frac{-10\sqrt{2}i+60}{2}$$

Divide 60-10i\sqrt{2} by 2.

$$x=-5\sqrt{2}i+30$$

The equation is now solved.

$$x=30+5\sqrt{2}i x=-5\sqrt{2}i+30$$

Steps for Completing the Square

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

$$x^{2}-60x+950=0$$

Subtract 950 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-60x=-950$$

Divide -60, the coefficient of the x term, by 2 to get -30. Then add the square of -30 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-60x+\left(-30\right)^{2}=-950+\left(-30\right)^{2}$$

Square -30.

$$x^{2}-60x+900=-950+900$$

Add -950 to 900.

$$x^{2}-60x+900=-50$$

Factor x^{2}-60x+900. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-30\right)^{2}=-50$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-30\right)^{2}}=\sqrt{-50}$$

Simplify.

$$x-30=5\sqrt{2}i x-30=-5\sqrt{2}i$$

Add 30 to both sides of the equation.

$$x=30+5\sqrt{2}i x=-5\sqrt{2}i+30$$