Solve 144^2-26^2=b^2

$$144 ^ { 2 } - 26 ^ { 2 } = b ^ { 2 }$$

Solve for b

$$b=2\sqrt{5015}\approx 141.633329411$$

$$b=-2\sqrt{5015}\approx -141.633329411$$

Steps by Finding Square Root

Calculate 144 to the power of 2 and get 20736.

$$20736-26^{2}=b^{2}$$

Calculate 26 to the power of 2 and get 676.

$$20736-676=b^{2}$$

Subtract 676 from 20736 to get 20060.

$$20060=b^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}=20060$$

Take the square root of both sides of the equation.

$$b=2\sqrt{5015} b=-2\sqrt{5015}$$

Steps Using the Quadratic Formula

Calculate 144 to the power of 2 and get 20736.

$$20736-26^{2}=b^{2}$$

Calculate 26 to the power of 2 and get 676.

$$20736-676=b^{2}$$

Subtract 676 from 20736 to get 20060.

$$20060=b^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}=20060$$

Subtract 20060 from both sides.

$$b^{2}-20060=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -20060 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-20060\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-20060\right)}}{2}$$

Multiply -4 times -20060.

$$b=\frac{0±\sqrt{80240}}{2}$$

Take the square root of 80240.

$$b=\frac{0±4\sqrt{5015}}{2}$$

Now solve the equation b=\frac{0±4\sqrt{5015}}{2} when ± is plus.

$$b=2\sqrt{5015}$$

Now solve the equation b=\frac{0±4\sqrt{5015}}{2} when ± is minus.

$$b=-2\sqrt{5015}$$

The equation is now solved.

$$b=2\sqrt{5015} b=-2\sqrt{5015}$$