Solve 864=6*(a)^2

$$864 = 6 \times ( a ) ^ { 2 }$$

Solve for a

$$a=12$$

$$a=-12$$

Steps Using Difference of Squares

Divide both sides by 6.

$$\frac{864}{6}=a^{2}$$

Divide 864 by 6 to get 144.

$$144=a^{2}$$

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

$$a^{2}=144$$

Subtract 144 from both sides.

$$a^{2}-144=0$$

Consider a^{2}-144. Rewrite a^{2}-144 as a^{2}-12^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-12\right)\left(a+12\right)=0$$

To find equation solutions, solve a-12=0 and a+12=0.

$$a=12 a=-12$$

Steps by Finding Square Root

Divide both sides by 6.

$$\frac{864}{6}=a^{2}$$

Divide 864 by 6 to get 144.

$$144=a^{2}$$

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

$$a^{2}=144$$

Take the square root of both sides of the equation.

$$a=12 a=-12$$

Steps Using the Quadratic Formula

Divide both sides by 6.

$$\frac{864}{6}=a^{2}$$

Divide 864 by 6 to get 144.

$$144=a^{2}$$

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

$$a^{2}=144$$

Subtract 144 from both sides.

$$a^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$

Multiply -4 times -144.

$$a=\frac{0±\sqrt{576}}{2}$$

Take the square root of 576.

$$a=\frac{0±24}{2}$$

Now solve the equation a=\frac{0±24}{2} when ± is plus. Divide 24 by 2.

$$a=12$$

Now solve the equation a=\frac{0±24}{2} when ± is minus. Divide -24 by 2.

$$a=-12$$

The equation is now solved.

$$a=12 a=-12$$