Solve 1/4x^2-36=0

$$\frac{ 1 }{ 4 } { x }^{ 2 } -36 = 0$$

Solve for x

$$x=12$$

$$x=-12$$

Steps Using Difference of Squares

Multiply both sides by 4.

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

Consider x^{2}-144. Rewrite x^{2}-144 as x^{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).

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

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

$$x=12 x=-12$$

Steps by Finding Square Root

Add 36 to both sides. Anything plus zero gives itself.

$$\frac{1}{4}x^{2}=36$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x^{2}=36\times 4$$

Multiply 36 and 4 to get 144.

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{1}{4}x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{4} for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{4}\left(-36\right)}}{2\times \frac{1}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{4}\left(-36\right)}}{2\times \frac{1}{4}}$$

Multiply -4 times \frac{1}{4}.

$$x=\frac{0±\sqrt{-\left(-36\right)}}{2\times \frac{1}{4}}$$

Multiply -1 times -36.

$$x=\frac{0±\sqrt{36}}{2\times \frac{1}{4}}$$

Take the square root of 36.

$$x=\frac{0±6}{2\times \frac{1}{4}}$$

Multiply 2 times \frac{1}{4}.

$$x=\frac{0±6}{\frac{1}{2}}$$

Now solve the equation x=\frac{0±6}{\frac{1}{2}} when ± is plus. Divide 6 by \frac{1}{2} by multiplying 6 by the reciprocal of \frac{1}{2}.

$$x=12$$

Now solve the equation x=\frac{0±6}{\frac{1}{2}} when ± is minus. Divide -6 by \frac{1}{2} by multiplying -6 by the reciprocal of \frac{1}{2}.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$