Solve 36x^2-100*(x^2-4)=0

$$36 { x }^{ 2 } -100 \times ( { x }^{ 2 } -4)=0$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps by Finding Square Root

Use the distributive property to multiply -100 by x^{2}-4.

$$36x^{2}-100x^{2}+400=0$$

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

$$-64x^{2}+400=0$$

Subtract 400 from both sides. Anything subtracted from zero gives its negation.

$$-64x^{2}=-400$$

Divide both sides by -64.

$$x^{2}=\frac{-400}{-64}$$

Reduce the fraction \frac{-400}{-64} to lowest terms by extracting and canceling out -16.

$$x^{2}=\frac{25}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -100 by x^{2}-4.

$$36x^{2}-100x^{2}+400=0$$

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

$$-64x^{2}+400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -64 for a, 0 for b, and 400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-64\right)\times 400}}{2\left(-64\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-64\right)\times 400}}{2\left(-64\right)}$$

Multiply -4 times -64.

$$x=\frac{0±\sqrt{256\times 400}}{2\left(-64\right)}$$

Multiply 256 times 400.

$$x=\frac{0±\sqrt{102400}}{2\left(-64\right)}$$

Take the square root of 102400.

$$x=\frac{0±320}{2\left(-64\right)}$$

Multiply 2 times -64.

$$x=\frac{0±320}{-128}$$

Now solve the equation x=\frac{0±320}{-128} when ± is plus. Reduce the fraction \frac{320}{-128} to lowest terms by extracting and canceling out 64.

$$x=-\frac{5}{2}$$

Now solve the equation x=\frac{0±320}{-128} when ± is minus. Reduce the fraction \frac{-320}{-128} to lowest terms by extracting and canceling out 64.

$$x=\frac{5}{2}$$

The equation is now solved.

$$x=-\frac{5}{2} x=\frac{5}{2}$$