Solve 36x^2-64=0

$$36 { x }^{ 2 } -64=0$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps Using Difference of Squares

Divide both sides by 4.

$$9x^{2}-16=0$$

Consider 9x^{2}-16. Rewrite 9x^{2}-16 as \left(3x\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-4\right)\left(3x+4\right)=0$$

To find equation solutions, solve 3x-4=0 and 3x+4=0.

$$x=\frac{4}{3} x=-\frac{4}{3}$$

Steps by Finding Square Root

Add 64 to both sides. Anything plus zero gives itself.

$$36x^{2}=64$$

Divide both sides by 36.

$$x^{2}=\frac{64}{36}$$

Reduce the fraction \frac{64}{36} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{16}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{4}{3} x=-\frac{4}{3}$$

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.

$$36x^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36\left(-64\right)}}{2\times 36}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 36\left(-64\right)}}{2\times 36}$$

Multiply -4 times 36.

$$x=\frac{0±\sqrt{-144\left(-64\right)}}{2\times 36}$$

Multiply -144 times -64.

$$x=\frac{0±\sqrt{9216}}{2\times 36}$$

Take the square root of 9216.

$$x=\frac{0±96}{2\times 36}$$

Multiply 2 times 36.

$$x=\frac{0±96}{72}$$

Now solve the equation x=\frac{0±96}{72} when ± is plus. Reduce the fraction \frac{96}{72} to lowest terms by extracting and canceling out 24.

$$x=\frac{4}{3}$$

Now solve the equation x=\frac{0±96}{72} when ± is minus. Reduce the fraction \frac{-96}{72} to lowest terms by extracting and canceling out 24.

$$x=-\frac{4}{3}$$

The equation is now solved.

$$x=\frac{4}{3} x=-\frac{4}{3}$$