Solve 6^2+b^2=100^2

$$6 ^ { 2 } + b ^ { 2 } = 100 ^ { 2 }$$

Solve for b

$$b=2\sqrt{2491}\approx 99.819837708$$

$$b=-2\sqrt{2491}\approx -99.819837708$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36+b^{2}=100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$36+b^{2}=10000$$

Subtract 36 from both sides.

$$b^{2}=10000-36$$

Subtract 36 from 10000 to get 9964.

$$b^{2}=9964$$

Take the square root of both sides of the equation.

$$b=2\sqrt{2491} b=-2\sqrt{2491}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36+b^{2}=100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$36+b^{2}=10000$$

Subtract 10000 from both sides.

$$36+b^{2}-10000=0$$

Subtract 10000 from 36 to get -9964.

$$-9964+b^{2}=0$$

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.

$$b^{2}-9964=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9964 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-9964\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-9964\right)}}{2}$$

Multiply -4 times -9964.

$$b=\frac{0±\sqrt{39856}}{2}$$

Take the square root of 39856.

$$b=\frac{0±4\sqrt{2491}}{2}$$

Now solve the equation b=\frac{0±4\sqrt{2491}}{2} when ± is plus.

$$b=2\sqrt{2491}$$

Now solve the equation b=\frac{0±4\sqrt{2491}}{2} when ± is minus.

$$b=-2\sqrt{2491}$$

The equation is now solved.

$$b=2\sqrt{2491} b=-2\sqrt{2491}$$