Solve 4^2=a^2+6^2

$$4 ^ { 2 } = a ^ { 2 } + 6 ^ { 2 }$$

Solve for a

$$a=-2\sqrt{5}i\approx -0-4.472135955i$$

$$a=2\sqrt{5}i\approx 4.472135955i$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16=a^{2}+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16=a^{2}+36$$

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

$$a^{2}+36=16$$

Subtract 36 from both sides.

$$a^{2}=16-36$$

Subtract 36 from 16 to get -20.

$$a^{2}=-20$$

The equation is now solved.

$$a=2\sqrt{5}i a=-2\sqrt{5}i$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16=a^{2}+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16=a^{2}+36$$

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

$$a^{2}+36=16$$

Subtract 16 from both sides.

$$a^{2}+36-16=0$$

Subtract 16 from 36 to get 20.

$$a^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 20}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 20}}{2}$$

Multiply -4 times 20.

$$a=\frac{0±\sqrt{-80}}{2}$$

Take the square root of -80.

$$a=\frac{0±4\sqrt{5}i}{2}$$

Now solve the equation a=\frac{0±4\sqrt{5}i}{2} when ± is plus.

$$a=2\sqrt{5}i$$

Now solve the equation a=\frac{0±4\sqrt{5}i}{2} when ± is minus.

$$a=-2\sqrt{5}i$$

The equation is now solved.

$$a=2\sqrt{5}i a=-2\sqrt{5}i$$