Solve 2^2=T^2+8^2

$${ 2 }^{ 2 } = { T }^{ 2 } + { 8 }^{ 2 }$$

Solve for T

$$T=-2\sqrt{15}i\approx -0-7.745966692i$$

$$T=2\sqrt{15}i\approx 7.745966692i$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$4=T^{2}+8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$4=T^{2}+64$$

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

$$T^{2}+64=4$$

Subtract 64 from both sides.

$$T^{2}=4-64$$

Subtract 64 from 4 to get -60.

$$T^{2}=-60$$

The equation is now solved.

$$T=2\sqrt{15}i T=-2\sqrt{15}i$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$4=T^{2}+8^{2}$$

Calculate 8 to the power of 2 and get 64.

$$4=T^{2}+64$$

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

$$T^{2}+64=4$$

Subtract 4 from both sides.

$$T^{2}+64-4=0$$

Subtract 4 from 64 to get 60.

$$T^{2}+60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$T=\frac{0±\sqrt{0^{2}-4\times 60}}{2}$$

Square 0.

$$T=\frac{0±\sqrt{-4\times 60}}{2}$$

Multiply -4 times 60.

$$T=\frac{0±\sqrt{-240}}{2}$$

Take the square root of -240.

$$T=\frac{0±4\sqrt{15}i}{2}$$

Now solve the equation T=\frac{0±4\sqrt{15}i}{2} when ± is plus.

$$T=2\sqrt{15}i$$

Now solve the equation T=\frac{0±4\sqrt{15}i}{2} when ± is minus.

$$T=-2\sqrt{15}i$$

The equation is now solved.

$$T=2\sqrt{15}i T=-2\sqrt{15}i$$