Solve 4-36x^2=0

$$4-36 { x }^{ 2 } =0$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps by Finding Square Root

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-36x^{2}=-4$$

Divide both sides by -36.

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

Reduce the fraction \frac{-4}{-36} to lowest terms by extracting and canceling out -4.

$$x^{2}=\frac{1}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{3} x=-\frac{1}{3}$$

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.

$$-36x^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144\times 4}}{2\left(-36\right)}$$

Multiply 144 times 4.

$$x=\frac{0±\sqrt{576}}{2\left(-36\right)}$$

Take the square root of 576.

$$x=\frac{0±24}{2\left(-36\right)}$$

Multiply 2 times -36.

$$x=\frac{0±24}{-72}$$

Now solve the equation x=\frac{0±24}{-72} when ± is plus. Reduce the fraction \frac{24}{-72} to lowest terms by extracting and canceling out 24.

$$x=-\frac{1}{3}$$

Now solve the equation x=\frac{0±24}{-72} when ± is minus. Reduce the fraction \frac{-24}{-72} to lowest terms by extracting and canceling out 24.

$$x=\frac{1}{3}$$

The equation is now solved.

$$x=-\frac{1}{3} x=\frac{1}{3}$$