Solve (63)^2+(84)^2=2t^2

$$( 63 ) ^ { 2 } + ( 84 ) ^ { 2 } = 2 t ^ { 2 }$$

Solve for t

$$t = \frac{105 \sqrt{2}}{2} \approx 74.246212025$$

$$t = -\frac{105 \sqrt{2}}{2} \approx -74.246212025$$

Steps by Finding Square Root

Calculate 63 to the power of 2 and get 3969.

$$3969+84^{2}=2t^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$3969+7056=2t^{2}$$

Add 3969 and 7056 to get 11025.

$$11025=2t^{2}$$

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

$$2t^{2}=11025$$

Divide both sides by 2.

$$t^{2}=\frac{11025}{2}$$

Take the square root of both sides of the equation.

$$t=\frac{105\sqrt{2}}{2} t=-\frac{105\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Calculate 63 to the power of 2 and get 3969.

$$3969+84^{2}=2t^{2}$$

Calculate 84 to the power of 2 and get 7056.

$$3969+7056=2t^{2}$$

Add 3969 and 7056 to get 11025.

$$11025=2t^{2}$$

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

$$2t^{2}=11025$$

Subtract 11025 from both sides.

$$2t^{2}-11025=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -11025 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times 2\left(-11025\right)}}{2\times 2}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times 2\left(-11025\right)}}{2\times 2}$$

Multiply -4 times 2.

$$t=\frac{0±\sqrt{-8\left(-11025\right)}}{2\times 2}$$

Multiply -8 times -11025.

$$t=\frac{0±\sqrt{88200}}{2\times 2}$$

Take the square root of 88200.

$$t=\frac{0±210\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$t=\frac{0±210\sqrt{2}}{4}$$

Now solve the equation t=\frac{0±210\sqrt{2}}{4} when ± is plus.

$$t=\frac{105\sqrt{2}}{2}$$

Now solve the equation t=\frac{0±210\sqrt{2}}{4} when ± is minus.

$$t=-\frac{105\sqrt{2}}{2}$$

The equation is now solved.

$$t=\frac{105\sqrt{2}}{2} t=-\frac{105\sqrt{2}}{2}$$