Solve 25^2=x^2+10^2

$$25 ^ { 2 } = x ^ { 2 } + 10 ^ { 2 }$$

Solve for x

$$x=5\sqrt{21}\approx 22.912878475$$

$$x=-5\sqrt{21}\approx -22.912878475$$

Steps by Finding Square Root

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$625=x^{2}+100$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+100=625$$

Subtract 100 from both sides.

$$x^{2}=625-100$$

Subtract 100 from 625 to get 525.

$$x^{2}=525$$

Take the square root of both sides of the equation.

$$x=5\sqrt{21} x=-5\sqrt{21}$$

Steps Using the Quadratic Formula

Calculate 25 to the power of 2 and get 625.

$$625=x^{2}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$625=x^{2}+100$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+100=625$$

Subtract 625 from both sides.

$$x^{2}+100-625=0$$

Subtract 625 from 100 to get -525.

$$x^{2}-525=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -525 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-525\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-525\right)}}{2}$$

Multiply -4 times -525.

$$x=\frac{0±\sqrt{2100}}{2}$$

Take the square root of 2100.

$$x=\frac{0±10\sqrt{21}}{2}$$

Now solve the equation x=\frac{0±10\sqrt{21}}{2} when ± is plus.

$$x=5\sqrt{21}$$

Now solve the equation x=\frac{0±10\sqrt{21}}{2} when ± is minus.

$$x=-5\sqrt{21}$$

The equation is now solved.

$$x=5\sqrt{21} x=-5\sqrt{21}$$