Solve (x+7/2)^2-53/2

$$( x + \frac { 7 } { 2 } ) ^ { 2 } - \frac { 53 } { 2 }$$

Evaluate

$$x^{2}+7x-\frac{57}{4}$$

Solution Steps

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

$$x^{2}+7x+\frac{49}{4}-\frac{53}{2}$$

Subtract \frac{53}{2} from \frac{49}{4} to get -\frac{57}{4}.

$$x^{2}+7x-\frac{57}{4}$$

Expand

$$x^{2}+7x-\frac{57}{4}$$

Solution Steps

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

$$x^{2}+7x+\frac{49}{4}-\frac{53}{2}$$

Subtract \frac{53}{2} from \frac{49}{4} to get -\frac{57}{4}.

$$x^{2}+7x-\frac{57}{4}$$