Solve 9^2=45^2+x^2

$${ 9 }^{ 2 } = { 45 }^{ 2 } + { x }^{ 2 }$$

Solve for x (complex solution)

$$x=-18\sqrt{6}i\approx -0-44.09081537i$$

$$x=18\sqrt{6}i\approx 44.09081537i$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$81=45^{2}+x^{2}$$

Calculate 45 to the power of 2 and get 2025.

$$81=2025+x^{2}$$

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

$$2025+x^{2}=81$$

Subtract 2025 from both sides.

$$x^{2}=81-2025$$

Subtract 2025 from 81 to get -1944.

$$x^{2}=-1944$$

The equation is now solved.

$$x=18\sqrt{6}i x=-18\sqrt{6}i$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$81=45^{2}+x^{2}$$

Calculate 45 to the power of 2 and get 2025.

$$81=2025+x^{2}$$

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

$$2025+x^{2}=81$$

Subtract 81 from both sides.

$$2025+x^{2}-81=0$$

Subtract 81 from 2025 to get 1944.

$$1944+x^{2}=0$$

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.

$$x^{2}+1944=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 1944 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1944}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1944}}{2}$$

Multiply -4 times 1944.

$$x=\frac{0±\sqrt{-7776}}{2}$$

Take the square root of -7776.

$$x=\frac{0±36\sqrt{6}i}{2}$$

Now solve the equation x=\frac{0±36\sqrt{6}i}{2} when ± is plus.

$$x=18\sqrt{6}i$$

Now solve the equation x=\frac{0±36\sqrt{6}i}{2} when ± is minus.

$$x=-18\sqrt{6}i$$

The equation is now solved.

$$x=18\sqrt{6}i x=-18\sqrt{6}i$$