Solve 15^2=17^2+x^2

$$15 ^ { 2 } = 17 ^ { 2 } + x ^ { 2 }$$

Solve for x (complex solution)

$$x=-8i$$

$$x=8i$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$225=17^{2}+x^{2}$$

Calculate 17 to the power of 2 and get 289.

$$225=289+x^{2}$$

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

$$289+x^{2}=225$$

Subtract 289 from both sides.

$$x^{2}=225-289$$

Subtract 289 from 225 to get -64.

$$x^{2}=-64$$

The equation is now solved.

$$x=8i x=-8i$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$225=17^{2}+x^{2}$$

Calculate 17 to the power of 2 and get 289.

$$225=289+x^{2}$$

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

$$289+x^{2}=225$$

Subtract 225 from both sides.

$$289+x^{2}-225=0$$

Subtract 225 from 289 to get 64.

$$64+x^{2}=0$$

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.

$$x^{2}+64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 64}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 64}}{2}$$

Multiply -4 times 64.

$$x=\frac{0±\sqrt{-256}}{2}$$

Take the square root of -256.

$$x=\frac{0±16i}{2}$$

Now solve the equation x=\frac{0±16i}{2} when ± is plus.

$$x=8i$$

Now solve the equation x=\frac{0±16i}{2} when ± is minus.

$$x=-8i$$

The equation is now solved.

$$x=8i x=-8i$$