Solve x^2+16x^2/9=25

$${ x }^{ 2 } + \frac{ 16 { x }^{ 2 } }{ 9 } =25$$

Solve for x

$$x=3$$

$$x=-3$$

Steps Using Difference of Squares

Multiply both sides of the equation by 9.

$$9x^{2}+16x^{2}=225$$

Combine 9x^{2} and 16x^{2} to get 25x^{2}.

$$25x^{2}=225$$

Subtract 225 from both sides.

$$25x^{2}-225=0$$

Divide both sides by 25.

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

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

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

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

$$x=3 x=-3$$

Steps by Finding Square Root

Multiply both sides of the equation by 9.

$$9x^{2}+16x^{2}=225$$

Combine 9x^{2} and 16x^{2} to get 25x^{2}.

$$25x^{2}=225$$

Divide both sides by 25.

$$x^{2}=\frac{225}{25}$$

Divide 225 by 25 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 9.

$$9x^{2}+16x^{2}=225$$

Combine 9x^{2} and 16x^{2} to get 25x^{2}.

$$25x^{2}=225$$

Subtract 225 from both sides.

$$25x^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-225\right)}}{2\times 25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-225\right)}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\left(-225\right)}}{2\times 25}$$

Multiply -100 times -225.

$$x=\frac{0±\sqrt{22500}}{2\times 25}$$

Take the square root of 22500.

$$x=\frac{0±150}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±150}{50}$$

Now solve the equation x=\frac{0±150}{50} when ± is plus. Divide 150 by 50.

$$x=3$$

Now solve the equation x=\frac{0±150}{50} when ± is minus. Divide -150 by 50.

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$