Solve 5x^2-4*8x=0

$$5 x ^ { 2 } - 4 \cdot 8 x = 0$$

Solve for x

$$x = \frac{32}{5} = 6\frac{2}{5} = 6.4$$

$$x=0$$

Steps Using Factoring

Multiply 4 and 8 to get 32.

$$5x^{2}-32x=0$$

Factor out x.

$$x\left(5x-32\right)=0$$

To find equation solutions, solve x=0 and 5x-32=0.

$$x=0 x=\frac{32}{5}$$

Steps Using the Quadratic Formula

Multiply 4 and 8 to get 32.

$$5x^{2}-32x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, -32 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}}}{2\times 5}$$

Take the square root of \left(-32\right)^{2}.

$$x=\frac{-\left(-32\right)±32}{2\times 5}$$

The opposite of -32 is 32.

$$x=\frac{32±32}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{32±32}{10}$$

Now solve the equation x=\frac{32±32}{10} when ± is plus. Add 32 to 32.

$$x=\frac{64}{10}$$

Reduce the fraction \frac{64}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{32}{5}$$

Now solve the equation x=\frac{32±32}{10} when ± is minus. Subtract 32 from 32.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

The equation is now solved.

$$x=\frac{32}{5} x=0$$

Steps for Completing the Square

Multiply 4 and 8 to get 32.

$$5x^{2}-32x=0$$

Divide both sides by 5.

$$\frac{5x^{2}-32x}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}-\frac{32}{5}x=\frac{0}{5}$$

Divide 0 by 5.

$$x^{2}-\frac{32}{5}x=0$$

Divide -\frac{32}{5}, the coefficient of the x term, by 2 to get -\frac{16}{5}. Then add the square of -\frac{16}{5} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{32}{5}x+\left(-\frac{16}{5}\right)^{2}=\left(-\frac{16}{5}\right)^{2}$$

Square -\frac{16}{5} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{32}{5}x+\frac{256}{25}=\frac{256}{25}$$

Factor x^{2}-\frac{32}{5}x+\frac{256}{25}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{16}{5}\right)^{2}=\frac{256}{25}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{16}{5}\right)^{2}}=\sqrt{\frac{256}{25}}$$

Simplify.

$$x-\frac{16}{5}=\frac{16}{5} x-\frac{16}{5}=-\frac{16}{5}$$

Add \frac{16}{5} to both sides of the equation.

$$x=\frac{32}{5} x=0$$