Solve x^2=25+625-x^2

$${ x }^{ 2 } =25+625- { x }^{ 2 }$$

Solve for x

$$x=5\sqrt{13}\approx 18.027756377$$

$$x=-5\sqrt{13}\approx -18.027756377$$

Steps by Finding Square Root

Add 25 and 625 to get 650.

$$x^{2}=650-x^{2}$$

Add x^{2} to both sides.

$$x^{2}+x^{2}=650$$

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

$$2x^{2}=650$$

Divide both sides by 2.

$$x^{2}=\frac{650}{2}$$

Divide 650 by 2 to get 325.

$$x^{2}=325$$

Take the square root of both sides of the equation.

$$x=5\sqrt{13} x=-5\sqrt{13}$$

Steps Using the Quadratic Formula

Add 25 and 625 to get 650.

$$x^{2}=650-x^{2}$$

Subtract 650 from both sides.

$$x^{2}-650=-x^{2}$$

Add x^{2} to both sides.

$$x^{2}-650+x^{2}=0$$

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

$$2x^{2}-650=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -650 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-650\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-650\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-650\right)}}{2\times 2}$$

Multiply -8 times -650.

$$x=\frac{0±\sqrt{5200}}{2\times 2}$$

Take the square root of 5200.

$$x=\frac{0±20\sqrt{13}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±20\sqrt{13}}{4}$$

Now solve the equation x=\frac{0±20\sqrt{13}}{4} when ± is plus.

$$x=5\sqrt{13}$$

Now solve the equation x=\frac{0±20\sqrt{13}}{4} when ± is minus.

$$x=-5\sqrt{13}$$

The equation is now solved.

$$x=5\sqrt{13} x=-5\sqrt{13}$$