Solve 5^2=4^2+b^2

$$5 ^ { 2 } = 4 ^ { 2 } + b ^ { 2 }$$

Solve for b

$$b=3$$

$$b=-3$$

Steps Using Difference of Squares

Calculate 5 to the power of 2 and get 25.

$$25=4^{2}+b^{2}$$

Calculate 4 to the power of 2 and get 16.

$$25=16+b^{2}$$

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

$$16+b^{2}=25$$

Subtract 25 from both sides.

$$16+b^{2}-25=0$$

Subtract 25 from 16 to get -9.

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

Consider -9+b^{2}. Rewrite -9+b^{2} as b^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(b-3\right)\left(b+3\right)=0$$

To find equation solutions, solve b-3=0 and b+3=0.

$$b=3 b=-3$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$25=4^{2}+b^{2}$$

Calculate 4 to the power of 2 and get 16.

$$25=16+b^{2}$$

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

$$16+b^{2}=25$$

Subtract 16 from both sides.

$$b^{2}=25-16$$

Subtract 16 from 25 to get 9.

$$b^{2}=9$$

Take the square root of both sides of the equation.

$$b=3 b=-3$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$25=4^{2}+b^{2}$$

Calculate 4 to the power of 2 and get 16.

$$25=16+b^{2}$$

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

$$16+b^{2}=25$$

Subtract 25 from both sides.

$$16+b^{2}-25=0$$

Subtract 25 from 16 to get -9.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-9\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$b=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$b=\frac{0±6}{2}$$

Now solve the equation b=\frac{0±6}{2} when ± is plus. Divide 6 by 2.

$$b=3$$

Now solve the equation b=\frac{0±6}{2} when ± is minus. Divide -6 by 2.

$$b=-3$$

The equation is now solved.

$$b=3 b=-3$$