Solve 8^2+b^2=22^2

$$8 ^ { 2 } + b ^ { 2 } = 22 ^ { 2 }$$

Solve for b

$$b=2\sqrt{105}\approx 20.493901532$$

$$b=-2\sqrt{105}\approx -20.493901532$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64+b^{2}=22^{2}$$

Calculate 22 to the power of 2 and get 484.

$$64+b^{2}=484$$

Subtract 64 from both sides.

$$b^{2}=484-64$$

Subtract 64 from 484 to get 420.

$$b^{2}=420$$

Take the square root of both sides of the equation.

$$b=2\sqrt{105} b=-2\sqrt{105}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64+b^{2}=22^{2}$$

Calculate 22 to the power of 2 and get 484.

$$64+b^{2}=484$$

Subtract 484 from both sides.

$$64+b^{2}-484=0$$

Subtract 484 from 64 to get -420.

$$-420+b^{2}=0$$

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.

$$b^{2}-420=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -420 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-420\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-420\right)}}{2}$$

Multiply -4 times -420.

$$b=\frac{0±\sqrt{1680}}{2}$$

Take the square root of 1680.

$$b=\frac{0±4\sqrt{105}}{2}$$

Now solve the equation b=\frac{0±4\sqrt{105}}{2} when ± is plus.

$$b=2\sqrt{105}$$

Now solve the equation b=\frac{0±4\sqrt{105}}{2} when ± is minus.

$$b=-2\sqrt{105}$$

The equation is now solved.

$$b=2\sqrt{105} b=-2\sqrt{105}$$