Solve b^2=8.5^2-4^2

$$b ^ { 2 } = 8.5 ^ { 2 } - 4 ^ { 2 }$$

Solve for b

$$b=7.5$$

$$b=-7.5$$

Steps Using Difference of Squares

Calculate 8.5 to the power of 2 and get 72.25.

$$b^{2}=72.25-4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$b^{2}=72.25-16$$

Subtract 16 from 72.25 to get 56.25.

$$b^{2}=56.25$$

Subtract 56.25 from both sides.

$$b^{2}-56.25=0$$

Consider b^{2}-56.25. Rewrite b^{2}-56.25 as b^{2}-\left(\frac{15}{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(b-\frac{15}{2}\right)\left(b+\frac{15}{2}\right)=0$$

To find equation solutions, solve b-\frac{15}{2}=0 and b+\frac{15}{2}=0.

$$b=\frac{15}{2} b=-\frac{15}{2}$$

Steps by Finding Square Root

Calculate 8.5 to the power of 2 and get 72.25.

$$b^{2}=72.25-4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$b^{2}=72.25-16$$

Subtract 16 from 72.25 to get 56.25.

$$b^{2}=56.25$$

Take the square root of both sides of the equation.

$$b=\frac{15}{2} b=-\frac{15}{2}$$

Steps Using the Quadratic Formula

Calculate 8.5 to the power of 2 and get 72.25.

$$b^{2}=72.25-4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$b^{2}=72.25-16$$

Subtract 16 from 72.25 to get 56.25.

$$b^{2}=56.25$$

Subtract 56.25 from both sides.

$$b^{2}-56.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -56.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-56.25\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-56.25\right)}}{2}$$

Multiply -4 times -56.25.

$$b=\frac{0±\sqrt{225}}{2}$$

Take the square root of 225.

$$b=\frac{0±15}{2}$$

Now solve the equation b=\frac{0±15}{2} when ± is plus. Divide 15 by 2.

$$b=\frac{15}{2}$$

Now solve the equation b=\frac{0±15}{2} when ± is minus. Divide -15 by 2.

$$b=-\frac{15}{2}$$

The equation is now solved.

$$b=\frac{15}{2} b=-\frac{15}{2}$$