Solve 1^2+b^2=3^2

$$1 ^ { 2 } + b ^ { 2 } = 3 ^ { 2 }$$

Solve for b

$$b=2\sqrt{2}\approx 2.828427125$$

$$b=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Calculate 1 to the power of 2 and get 1.

$$1+b^{2}=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$1+b^{2}=9$$

Subtract 1 from both sides.

$$b^{2}=9-1$$

Subtract 1 from 9 to get 8.

$$b^{2}=8$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate 1 to the power of 2 and get 1.

$$1+b^{2}=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$1+b^{2}=9$$

Subtract 9 from both sides.

$$1+b^{2}-9=0$$

Subtract 9 from 1 to get -8.

$$-8+b^{2}=0$$

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.

$$b^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-8\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-8\right)}}{2}$$

Multiply -4 times -8.

$$b=\frac{0±\sqrt{32}}{2}$$

Take the square root of 32.

$$b=\frac{0±4\sqrt{2}}{2}$$

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

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

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

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

The equation is now solved.

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