Solve 25x^2+36x^2-900=0

$$25 x ^ { 2 } + 36 x ^ { 2 } - 900 = 0$$

Solve for x

$$x = \frac{30 \sqrt{61}}{61} \approx 3.841106398$$

$$x = -\frac{30 \sqrt{61}}{61} \approx -3.841106398$$

Steps by Finding Square Root

Combine 25x^{2} and 36x^{2} to get 61x^{2}.

$$61x^{2}-900=0$$

Add 900 to both sides. Anything plus zero gives itself.

$$61x^{2}=900$$

Divide both sides by 61.

$$x^{2}=\frac{900}{61}$$

Take the square root of both sides of the equation.

$$x=\frac{30\sqrt{61}}{61} x=-\frac{30\sqrt{61}}{61}$$

Steps Using the Quadratic Formula

Combine 25x^{2} and 36x^{2} to get 61x^{2}.

$$61x^{2}-900=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 61 for a, 0 for b, and -900 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 61\left(-900\right)}}{2\times 61}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 61\left(-900\right)}}{2\times 61}$$

Multiply -4 times 61.

$$x=\frac{0±\sqrt{-244\left(-900\right)}}{2\times 61}$$

Multiply -244 times -900.

$$x=\frac{0±\sqrt{219600}}{2\times 61}$$

Take the square root of 219600.

$$x=\frac{0±60\sqrt{61}}{2\times 61}$$

Multiply 2 times 61.

$$x=\frac{0±60\sqrt{61}}{122}$$

Now solve the equation x=\frac{0±60\sqrt{61}}{122} when ± is plus.

$$x=\frac{30\sqrt{61}}{61}$$

Now solve the equation x=\frac{0±60\sqrt{61}}{122} when ± is minus.

$$x=-\frac{30\sqrt{61}}{61}$$

The equation is now solved.

$$x=\frac{30\sqrt{61}}{61} x=-\frac{30\sqrt{61}}{61}$$