Solve 3^2=25^2+x^2

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

Solve for x (complex solution)

$$x=-2\sqrt{154}i\approx -0-24.819347292i$$

$$x=2\sqrt{154}i\approx 24.819347292i$$

Steps by Finding Square Root

Calculate 3 to the power of 2 and get 9.

$$9=25^{2}+x^{2}$$

Calculate 25 to the power of 2 and get 625.

$$9=625+x^{2}$$

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

$$625+x^{2}=9$$

Subtract 625 from both sides.

$$x^{2}=9-625$$

Subtract 625 from 9 to get -616.

$$x^{2}=-616$$

The equation is now solved.

$$x=2\sqrt{154}i x=-2\sqrt{154}i$$

Steps Using the Quadratic Formula

Calculate 3 to the power of 2 and get 9.

$$9=25^{2}+x^{2}$$

Calculate 25 to the power of 2 and get 625.

$$9=625+x^{2}$$

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

$$625+x^{2}=9$$

Subtract 9 from both sides.

$$625+x^{2}-9=0$$

Subtract 9 from 625 to get 616.

$$616+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+616=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 616 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 616}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 616}}{2}$$

Multiply -4 times 616.

$$x=\frac{0±\sqrt{-2464}}{2}$$

Take the square root of -2464.

$$x=\frac{0±4\sqrt{154}i}{2}$$

Now solve the equation x=\frac{0±4\sqrt{154}i}{2} when ± is plus.

$$x=2\sqrt{154}i$$

Now solve the equation x=\frac{0±4\sqrt{154}i}{2} when ± is minus.

$$x=-2\sqrt{154}i$$

The equation is now solved.

$$x=2\sqrt{154}i x=-2\sqrt{154}i$$