Solve 64x^2+36x^2-12=0

$$64 { x }^{ 2 } +36 { x }^{ 2 } -12=0$$

Solve for x

$$x=\frac{\sqrt{3}}{5}\approx 0.346410162$$

$$x=-\frac{\sqrt{3}}{5}\approx -0.346410162$$

Steps by Finding Square Root

Combine 64x^{2} and 36x^{2} to get 100x^{2}.

$$100x^{2}-12=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$100x^{2}=12$$

Divide both sides by 100.

$$x^{2}=\frac{12}{100}$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{3}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{5} x=-\frac{\sqrt{3}}{5}$$

Steps Using the Quadratic Formula

Combine 64x^{2} and 36x^{2} to get 100x^{2}.

$$100x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-12\right)}}{2\times 100}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 100\left(-12\right)}}{2\times 100}$$

Multiply -4 times 100.

$$x=\frac{0±\sqrt{-400\left(-12\right)}}{2\times 100}$$

Multiply -400 times -12.

$$x=\frac{0±\sqrt{4800}}{2\times 100}$$

Take the square root of 4800.

$$x=\frac{0±40\sqrt{3}}{2\times 100}$$

Multiply 2 times 100.

$$x=\frac{0±40\sqrt{3}}{200}$$

Now solve the equation x=\frac{0±40\sqrt{3}}{200} when ± is plus.

$$x=\frac{\sqrt{3}}{5}$$

Now solve the equation x=\frac{0±40\sqrt{3}}{200} when ± is minus.

$$x=-\frac{\sqrt{3}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{5} x=-\frac{\sqrt{3}}{5}$$