Solve 4^2+b^2=6^2

$$4 ^ { 2 } + b ^ { 2 } = 6 ^ { 2 }$$

Solve for b

$$b=2\sqrt{5}\approx 4.472135955$$

$$b=-2\sqrt{5}\approx -4.472135955$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16+b^{2}=6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16+b^{2}=36$$

Subtract 16 from both sides.

$$b^{2}=36-16$$

Subtract 16 from 36 to get 20.

$$b^{2}=20$$

Take the square root of both sides of the equation.

$$b=2\sqrt{5} b=-2\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16+b^{2}=6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16+b^{2}=36$$

Subtract 36 from both sides.

$$16+b^{2}-36=0$$

Subtract 36 from 16 to get -20.

$$-20+b^{2}=0$$

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.

$$b^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-20\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-20\right)}}{2}$$

Multiply -4 times -20.

$$b=\frac{0±\sqrt{80}}{2}$$

Take the square root of 80.

$$b=\frac{0±4\sqrt{5}}{2}$$

Now solve the equation b=\frac{0±4\sqrt{5}}{2} when ± is plus.

$$b=2\sqrt{5}$$

Now solve the equation b=\frac{0±4\sqrt{5}}{2} when ± is minus.

$$b=-2\sqrt{5}$$

The equation is now solved.

$$b=2\sqrt{5} b=-2\sqrt{5}$$