Solve 64(300^2+x^2)=100x^2

$$64 ( 300 ^ { 2 } + x ^ { 2 } ) = 100 x ^ { 2 }$$

Solve for x

$$x=400$$

$$x=-400$$

Steps by Finding Square Root

Calculate 300 to the power of 2 and get 90000.

$$64\left(90000+x^{2}\right)=100x^{2}$$

Use the distributive property to multiply 64 by 90000+x^{2}.

$$5760000+64x^{2}=100x^{2}$$

Subtract 100x^{2} from both sides.

$$5760000+64x^{2}-100x^{2}=0$$

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

$$5760000-36x^{2}=0$$

Subtract 5760000 from both sides. Anything subtracted from zero gives its negation.

$$-36x^{2}=-5760000$$

Divide both sides by -36.

$$x^{2}=\frac{-5760000}{-36}$$

Divide -5760000 by -36 to get 160000.

$$x^{2}=160000$$

Take the square root of both sides of the equation.

$$x=400 x=-400$$

Steps Using the Quadratic Formula

Calculate 300 to the power of 2 and get 90000.

$$64\left(90000+x^{2}\right)=100x^{2}$$

Use the distributive property to multiply 64 by 90000+x^{2}.

$$5760000+64x^{2}=100x^{2}$$

Subtract 100x^{2} from both sides.

$$5760000+64x^{2}-100x^{2}=0$$

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

$$5760000-36x^{2}=0$$

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.

$$-36x^{2}+5760000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -36 for a, 0 for b, and 5760000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)\times 5760000}}{2\left(-36\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)\times 5760000}}{2\left(-36\right)}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144\times 5760000}}{2\left(-36\right)}$$

Multiply 144 times 5760000.

$$x=\frac{0±\sqrt{829440000}}{2\left(-36\right)}$$

Take the square root of 829440000.

$$x=\frac{0±28800}{2\left(-36\right)}$$

Multiply 2 times -36.

$$x=\frac{0±28800}{-72}$$

Now solve the equation x=\frac{0±28800}{-72} when ± is plus. Divide 28800 by -72.

$$x=-400$$

Now solve the equation x=\frac{0±28800}{-72} when ± is minus. Divide -28800 by -72.

$$x=400$$

The equation is now solved.

$$x=-400 x=400$$