Solve (x+1/2)^2-5

$$( x + \frac { 1 } { 2 } ) ^ { 2 } - 5$$

Evaluate

$$x^{2}+x-\frac{19}{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{2}\right)^{2}.

$$x^{2}+x+\frac{1}{4}-5$$

Subtract 5 from \frac{1}{4} to get -\frac{19}{4}.

$$x^{2}+x-\frac{19}{4}$$

Expand

$$x^{2}+x-\frac{19}{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{2}\right)^{2}.

$$x^{2}+x+\frac{1}{4}-5$$

Subtract 5 from \frac{1}{4} to get -\frac{19}{4}.

$$x^{2}+x-\frac{19}{4}$$