Solve 0=4*x^2-64x

$$0=4 \times { x }^{ 2 } -64x$$

Solve for x

$$x=16$$

$$x=0$$

Steps Using Factoring

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

$$4x^{2}-64x=0$$

Factor out x.

$$x\left(4x-64\right)=0$$

To find equation solutions, solve x=0 and 4x-64=0.

$$x=0 x=16$$

Steps Using the Quadratic Formula

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

$$4x^{2}-64x=0$$

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

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}}}{2\times 4}$$

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

$$x=\frac{-\left(-64\right)±64}{2\times 4}$$

The opposite of -64 is 64.

$$x=\frac{64±64}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{64±64}{8}$$

Now solve the equation x=\frac{64±64}{8} when ± is plus. Add 64 to 64.

$$x=\frac{128}{8}$$

Divide 128 by 8.

$$x=16$$

Now solve the equation x=\frac{64±64}{8} when ± is minus. Subtract 64 from 64.

$$x=\frac{0}{8}$$

Divide 0 by 8.

$$x=0$$

The equation is now solved.

$$x=16 x=0$$

Steps for Completing the Square

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

$$4x^{2}-64x=0$$

Divide both sides by 4.

$$\frac{4x^{2}-64x}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\left(-\frac{64}{4}\right)x=\frac{0}{4}$$

Divide -64 by 4.

$$x^{2}-16x=\frac{0}{4}$$

Divide 0 by 4.

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

Divide -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-16x+\left(-8\right)^{2}=\left(-8\right)^{2}$$

Square -8.

$$x^{2}-16x+64=64$$

Factor x^{2}-16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-8\right)^{2}=64$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{64}$$

Simplify.

$$x-8=8 x-8=-8$$

Add 8 to both sides of the equation.

$$x=16 x=0$$