Solve x^2=84^2+58^2

$$x ^ { 2 } = 84 ^ { 2 } + 58 ^ { 2 }$$

Solve for x

$$x=2\sqrt{2605}\approx 102.078401241$$

$$x=-2\sqrt{2605}\approx -102.078401241$$

Steps by Finding Square Root

Calculate 84 to the power of 2 and get 7056.

$$x^{2}=7056+58^{2}$$

Calculate 58 to the power of 2 and get 3364.

$$x^{2}=7056+3364$$

Add 7056 and 3364 to get 10420.

$$x^{2}=10420$$

Take the square root of both sides of the equation.

$$x=2\sqrt{2605} x=-2\sqrt{2605}$$

Steps Using the Quadratic Formula

Calculate 84 to the power of 2 and get 7056.

$$x^{2}=7056+58^{2}$$

Calculate 58 to the power of 2 and get 3364.

$$x^{2}=7056+3364$$

Add 7056 and 3364 to get 10420.

$$x^{2}=10420$$

Subtract 10420 from both sides.

$$x^{2}-10420=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -10420 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-10420\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-10420\right)}}{2}$$

Multiply -4 times -10420.

$$x=\frac{0±\sqrt{41680}}{2}$$

Take the square root of 41680.

$$x=\frac{0±4\sqrt{2605}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{2605}}{2} when ± is plus.

$$x=2\sqrt{2605}$$

Now solve the equation x=\frac{0±4\sqrt{2605}}{2} when ± is minus.

$$x=-2\sqrt{2605}$$

The equation is now solved.

$$x=2\sqrt{2605} x=-2\sqrt{2605}$$