Solve m(m+7/2)=100-(m+7/2)^2

$$m ( m + \frac { 7 } { 2 } ) = 100 - ( m + \frac { 7 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{351}{4}-7m-m^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+\frac{7}{2}\right)^{2}.

$$100-\left(m^{2}+7m+\frac{49}{4}\right)$$

To find the opposite of m^{2}+7m+\frac{49}{4}, find the opposite of each term.

$$100-m^{2}-7m-\frac{49}{4}$$

Subtract \frac{49}{4} from 100 to get \frac{351}{4}.

$$\frac{351}{4}-m^{2}-7m$$

Expand

$$\frac{351}{4}-7m-m^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+\frac{7}{2}\right)^{2}.

$$100-\left(m^{2}+7m+\frac{49}{4}\right)$$

To find the opposite of m^{2}+7m+\frac{49}{4}, find the opposite of each term.

$$100-m^{2}-7m-\frac{49}{4}$$

Subtract \frac{49}{4} from 100 to get \frac{351}{4}.

$$\frac{351}{4}-m^{2}-7m$$