Solve x=0^2-60^2/2x-2^2

$$x = \frac { 0 ^ { 2 } - 60 ^ { 2 } } { 2 x - 2 ^ { 2 } }$$

Solve for x (complex solution)

$$x=1+\sqrt{1799}i\approx 1+42.414620121i$$

$$x=-\sqrt{1799}i+1\approx 1-42.414620121i$$

Steps Using the Quadratic Formula

Calculate 0 to the power of 2 and get 0.

$$x=\frac{0-60^{2}}{2x-2^{2}}$$

Calculate 60 to the power of 2 and get 3600.

$$x=\frac{0-3600}{2x-2^{2}}$$

Subtract 3600 from 0 to get -3600.

$$x=\frac{-3600}{2x-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$x=\frac{-3600}{2x-4}$$

Subtract \frac{-3600}{2x-4} from both sides.

$$x-\frac{-3600}{2x-4}=0$$

Factor 2x-4.

$$x-\frac{-3600}{2\left(x-2\right)}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2\left(x-2\right)}{2\left(x-2\right)}.

$$\frac{x\times 2\left(x-2\right)}{2\left(x-2\right)}-\frac{-3600}{2\left(x-2\right)}=0$$

Since \frac{x\times 2\left(x-2\right)}{2\left(x-2\right)} and \frac{-3600}{2\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 2\left(x-2\right)-\left(-3600\right)}{2\left(x-2\right)}=0$$

Do the multiplications in x\times 2\left(x-2\right)-\left(-3600\right).

$$\frac{2x^{2}-4x+3600}{2\left(x-2\right)}=0$$

Factor the expressions that are not already factored in \frac{2x^{2}-4x+3600}{2\left(x-2\right)}.

$$\frac{2\left(x^{2}-2x+1800\right)}{2\left(x-2\right)}=0$$

Cancel out 2 in both numerator and denominator.

$$\frac{x^{2}-2x+1800}{x-2}=0$$

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$x^{2}-2x+1800=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -2 for b, and 1800 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 1800}}{2}$$

Square -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 1800}}{2}$$

Multiply -4 times 1800.

$$x=\frac{-\left(-2\right)±\sqrt{4-7200}}{2}$$

Add 4 to -7200.

$$x=\frac{-\left(-2\right)±\sqrt{-7196}}{2}$$

Take the square root of -7196.

$$x=\frac{-\left(-2\right)±2\sqrt{1799}i}{2}$$

The opposite of -2 is 2.

$$x=\frac{2±2\sqrt{1799}i}{2}$$

Now solve the equation x=\frac{2±2\sqrt{1799}i}{2} when ± is plus. Add 2 to 2i\sqrt{1799}.

$$x=\frac{2+2\sqrt{1799}i}{2}$$

Divide 2+2i\sqrt{1799} by 2.

$$x=1+\sqrt{1799}i$$

Now solve the equation x=\frac{2±2\sqrt{1799}i}{2} when ± is minus. Subtract 2i\sqrt{1799} from 2.

$$x=\frac{-2\sqrt{1799}i+2}{2}$$

Divide 2-2i\sqrt{1799} by 2.

$$x=-\sqrt{1799}i+1$$

The equation is now solved.

$$x=1+\sqrt{1799}i x=-\sqrt{1799}i+1$$

Steps for Completing the Square

Calculate 0 to the power of 2 and get 0.

$$x=\frac{0-60^{2}}{2x-2^{2}}$$

Calculate 60 to the power of 2 and get 3600.

$$x=\frac{0-3600}{2x-2^{2}}$$

Subtract 3600 from 0 to get -3600.

$$x=\frac{-3600}{2x-2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$x=\frac{-3600}{2x-4}$$

Subtract \frac{-3600}{2x-4} from both sides.

$$x-\frac{-3600}{2x-4}=0$$

Factor 2x-4.

$$x-\frac{-3600}{2\left(x-2\right)}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2\left(x-2\right)}{2\left(x-2\right)}.

$$\frac{x\times 2\left(x-2\right)}{2\left(x-2\right)}-\frac{-3600}{2\left(x-2\right)}=0$$

Since \frac{x\times 2\left(x-2\right)}{2\left(x-2\right)} and \frac{-3600}{2\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 2\left(x-2\right)-\left(-3600\right)}{2\left(x-2\right)}=0$$

Do the multiplications in x\times 2\left(x-2\right)-\left(-3600\right).

$$\frac{2x^{2}-4x+3600}{2\left(x-2\right)}=0$$

Factor the expressions that are not already factored in \frac{2x^{2}-4x+3600}{2\left(x-2\right)}.

$$\frac{2\left(x^{2}-2x+1800\right)}{2\left(x-2\right)}=0$$

Cancel out 2 in both numerator and denominator.

$$\frac{x^{2}-2x+1800}{x-2}=0$$

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$x^{2}-2x+1800=0$$

Subtract 1800 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-2x=-1800$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-2x+1=-1800+1$$

Add -1800 to 1.

$$x^{2}-2x+1=-1799$$

Factor x^{2}-2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-1\right)^{2}=-1799$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{-1799}$$

Simplify.

$$x-1=\sqrt{1799}i x-1=-\sqrt{1799}i$$

Add 1 to both sides of the equation.

$$x=1+\sqrt{1799}i x=-\sqrt{1799}i+1$$