Solve 4x^2=x^2+25

$$4 x ^ { 2 } = x ^ { 2 } + 25$$

Solve for x

$$x = \frac{5 \sqrt{3}}{3} \approx 2.886751346$$

$$x = -\frac{5 \sqrt{3}}{3} \approx -2.886751346$$

Steps by Finding Square Root

Subtract x^{2} from both sides.

$$4x^{2}-x^{2}=25$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}=25$$

Divide both sides by 3.

$$x^{2}=\frac{25}{3}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract x^{2} from both sides.

$$4x^{2}-x^{2}=25$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}=25$$

Subtract 25 from both sides.

$$3x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-25\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-25\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-25\right)}}{2\times 3}$$

Multiply -12 times -25.

$$x=\frac{0±\sqrt{300}}{2\times 3}$$

Take the square root of 300.

$$x=\frac{0±10\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±10\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±10\sqrt{3}}{6} when ± is plus.

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

Now solve the equation x=\frac{0±10\sqrt{3}}{6} when ± is minus.

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

The equation is now solved.

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