Solve x^2=64x

$$x ^ { 2 } = 64 x$$

Solve for x

$$x=64$$

$$x=0$$

Steps Using Factoring

Subtract 64x from both sides.

$$x^{2}-64x=0$$

Factor out x.

$$x\left(x-64\right)=0$$

To find equation solutions, solve x=0 and x-64=0.

$$x=0 x=64$$

Steps Using the Quadratic Formula

Subtract 64x from both sides.

$$x^{2}-64x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -64 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}}}{2}$$

Take the square root of \left(-64\right)^{2}.

$$x=\frac{-\left(-64\right)±64}{2}$$

The opposite of -64 is 64.

$$x=\frac{64±64}{2}$$

Now solve the equation x=\frac{64±64}{2} when ± is plus. Add 64 to 64.

$$x=\frac{128}{2}$$

Divide 128 by 2.

$$x=64$$

Now solve the equation x=\frac{64±64}{2} when ± is minus. Subtract 64 from 64.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=64 x=0$$

Steps for Completing the Square

Subtract 64x from both sides.

$$x^{2}-64x=0$$

Divide -64, the coefficient of the x term, by 2 to get -32. Then add the square of -32 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-64x+\left(-32\right)^{2}=\left(-32\right)^{2}$$

Square -32.

$$x^{2}-64x+1024=1024$$

Factor x^{2}-64x+1024. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-32\right)^{2}=1024$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-32\right)^{2}}=\sqrt{1024}$$

Simplify.

$$x-32=32 x-32=-32$$

Add 32 to both sides of the equation.

$$x=64 x=0$$