Solve 11^2+b^2=15^2

$$11 ^ { 2 } + b ^ { 2 } = 15 ^ { 2 }$$

Solve for b

$$b=2\sqrt{26}\approx 10.198039027$$

$$b=-2\sqrt{26}\approx -10.198039027$$

Steps by Finding Square Root

Calculate 11 to the power of 2 and get 121.

$$121+b^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$121+b^{2}=225$$

Subtract 121 from both sides.

$$b^{2}=225-121$$

Subtract 121 from 225 to get 104.

$$b^{2}=104$$

Take the square root of both sides of the equation.

$$b=2\sqrt{26} b=-2\sqrt{26}$$

Steps Using the Quadratic Formula

Calculate 11 to the power of 2 and get 121.

$$121+b^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$121+b^{2}=225$$

Subtract 225 from both sides.

$$121+b^{2}-225=0$$

Subtract 225 from 121 to get -104.

$$-104+b^{2}=0$$

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.

$$b^{2}-104=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -104 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-104\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-104\right)}}{2}$$

Multiply -4 times -104.

$$b=\frac{0±\sqrt{416}}{2}$$

Take the square root of 416.

$$b=\frac{0±4\sqrt{26}}{2}$$

Now solve the equation b=\frac{0±4\sqrt{26}}{2} when ± is plus.

$$b=2\sqrt{26}$$

Now solve the equation b=\frac{0±4\sqrt{26}}{2} when ± is minus.

$$b=-2\sqrt{26}$$

The equation is now solved.

$$b=2\sqrt{26} b=-2\sqrt{26}$$