Solve -{left(x-1/2right)}^2+3/4

$$- { \left(x- \frac{ 1 }{ 2 } \right) }^{ 2 } + \frac{ 3 }{ 4 }$$

Evaluate

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

Solution Steps

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

$$-\left(x^{2}-x+\frac{1}{4}\right)+\frac{3}{4}$$

To find the opposite of x^{2}-x+\frac{1}{4}, find the opposite of each term.

$$-x^{2}+x-\frac{1}{4}+\frac{3}{4}$$

Add -\frac{1}{4} and \frac{3}{4} to get \frac{1}{2}.

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

Expand

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

Solution Steps

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

$$-\left(x^{2}-x+\frac{1}{4}\right)+\frac{3}{4}$$

To find the opposite of x^{2}-x+\frac{1}{4}, find the opposite of each term.

$$-x^{2}+x-\frac{1}{4}+\frac{3}{4}$$

Add -\frac{1}{4} and \frac{3}{4} to get \frac{1}{2}.

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