Solve x^2+50=25+2x^2

$$x ^ { 2 } + 50 = 25 + 2 x ^ { 2 }$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

Subtract 2x^{2} from both sides.

$$x^{2}+50-2x^{2}=25$$

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

$$-x^{2}+50=25$$

Subtract 50 from both sides.

$$-x^{2}=25-50$$

Subtract 50 from 25 to get -25.

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

Divide both sides by -1.

$$x^{2}=\frac{-25}{-1}$$

Fraction \frac{-25}{-1} can be simplified to 25 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Subtract 25 from both sides.

$$x^{2}+50-25=2x^{2}$$

Subtract 25 from 50 to get 25.

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

Subtract 2x^{2} from both sides.

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

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

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 25}}{2\left(-1\right)}$$

Multiply 4 times 25.

$$x=\frac{0±\sqrt{100}}{2\left(-1\right)}$$

Take the square root of 100.

$$x=\frac{0±10}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±10}{-2}$$

Now solve the equation x=\frac{0±10}{-2} when ± is plus. Divide 10 by -2.

$$x=-5$$

Now solve the equation x=\frac{0±10}{-2} when ± is minus. Divide -10 by -2.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$