Solve -4=64a^2/4a

$$- 4 = \frac { 64 a ^ { 2 } } { 4 a }$$

Solve for a

$$a=-\frac{1}{4}=-0.25$$

Steps Using Factoring

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4a.

$$-16a=64a^{2}$$

Subtract 64a^{2} from both sides.

$$-16a-64a^{2}=0$$

Factor out a.

$$a\left(-16-64a\right)=0$$

To find equation solutions, solve a=0 and -16-64a=0.

$$a=0 a=-\frac{1}{4}$$

Variable a cannot be equal to 0.

$$a=-\frac{1}{4}$$

Steps Using the Quadratic Formula

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4a.

$$-16a=64a^{2}$$

Subtract 64a^{2} from both sides.

$$-16a-64a^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-64a^{2}-16a=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -64 for a, -16 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}}}{2\left(-64\right)}$$

Take the square root of \left(-16\right)^{2}.

$$a=\frac{-\left(-16\right)±16}{2\left(-64\right)}$$

The opposite of -16 is 16.

$$a=\frac{16±16}{2\left(-64\right)}$$

Multiply 2 times -64.

$$a=\frac{16±16}{-128}$$

Now solve the equation a=\frac{16±16}{-128} when ± is plus. Add 16 to 16.

$$a=\frac{32}{-128}$$

Reduce the fraction \frac{32}{-128} to lowest terms by extracting and canceling out 32.

$$a=-\frac{1}{4}$$

Now solve the equation a=\frac{16±16}{-128} when ± is minus. Subtract 16 from 16.

$$a=\frac{0}{-128}$$

Divide 0 by -128.

$$a=0$$

The equation is now solved.

$$a=-\frac{1}{4} a=0$$

Variable a cannot be equal to 0.

$$a=-\frac{1}{4}$$

Steps for Completing the Square

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4a.

$$-16a=64a^{2}$$

Subtract 64a^{2} from both sides.

$$-16a-64a^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-64a^{2}-16a=0$$

Divide both sides by -64.

$$\frac{-64a^{2}-16a}{-64}=\frac{0}{-64}$$

Dividing by -64 undoes the multiplication by -64.

$$a^{2}+\left(-\frac{16}{-64}\right)a=\frac{0}{-64}$$

Reduce the fraction \frac{-16}{-64} to lowest terms by extracting and canceling out 16.

$$a^{2}+\frac{1}{4}a=\frac{0}{-64}$$

Divide 0 by -64.

$$a^{2}+\frac{1}{4}a=0$$

Divide \frac{1}{4}, the coefficient of the x term, by 2 to get \frac{1}{8}. Then add the square of \frac{1}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$a^{2}+\frac{1}{4}a+\left(\frac{1}{8}\right)^{2}=\left(\frac{1}{8}\right)^{2}$$

Square \frac{1}{8} by squaring both the numerator and the denominator of the fraction.

$$a^{2}+\frac{1}{4}a+\frac{1}{64}=\frac{1}{64}$$

Factor a^{2}+\frac{1}{4}a+\frac{1}{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}.

$$\left(a+\frac{1}{8}\right)^{2}=\frac{1}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(a+\frac{1}{8}\right)^{2}}=\sqrt{\frac{1}{64}}$$

Simplify.

$$a+\frac{1}{8}=\frac{1}{8} a+\frac{1}{8}=-\frac{1}{8}$$

Subtract \frac{1}{8} from both sides of the equation.

$$a=0 a=-\frac{1}{4}$$

Variable a cannot be equal to 0.

$$a=-\frac{1}{4}$$