Solve 36x^2+9x^2=25

$$36 x ^ { 2 } + 9 x ^ { 2 } = 25$$

Solve for x

$$x=\frac{\sqrt{5}}{3}\approx 0.745355992$$

$$x=-\frac{\sqrt{5}}{3}\approx -0.745355992$$

Steps by Finding Square Root

Combine 36x^{2} and 9x^{2} to get 45x^{2}.

$$45x^{2}=25$$

Divide both sides by 45.

$$x^{2}=\frac{25}{45}$$

Reduce the fraction \frac{25}{45} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{5}{9}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Combine 36x^{2} and 9x^{2} to get 45x^{2}.

$$45x^{2}=25$$

Subtract 25 from both sides.

$$45x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 45 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 45\left(-25\right)}}{2\times 45}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 45\left(-25\right)}}{2\times 45}$$

Multiply -4 times 45.

$$x=\frac{0±\sqrt{-180\left(-25\right)}}{2\times 45}$$

Multiply -180 times -25.

$$x=\frac{0±\sqrt{4500}}{2\times 45}$$

Take the square root of 4500.

$$x=\frac{0±30\sqrt{5}}{2\times 45}$$

Multiply 2 times 45.

$$x=\frac{0±30\sqrt{5}}{90}$$

Now solve the equation x=\frac{0±30\sqrt{5}}{90} when ± is plus.

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

Now solve the equation x=\frac{0±30\sqrt{5}}{90} when ± is minus.

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

The equation is now solved.

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