Solve =-2[(x+1/4)^2-49/16]

$$= - 2 [ ( x + \frac { 1 } { 4 } ) ^ { 2 } - \frac { 49 } { 16 } ]$$

Evaluate

$$-\left(2x-3\right)\left(x+2\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{4}\right)^{2}.

$$-2\left(x^{2}+\frac{1}{2}x+\frac{1}{16}-\frac{49}{16}\right)$$

Subtract \frac{49}{16} from \frac{1}{16} to get -3.

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

Use the distributive property to multiply -2 by x^{2}+\frac{1}{2}x-3.

$$-2x^{2}-x+6$$

Expand

$$6-x-2x^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+\frac{1}{4}\right)^{2}.

$$-2\left(x^{2}+\frac{1}{2}x+\frac{1}{16}-\frac{49}{16}\right)$$

Subtract \frac{49}{16} from \frac{1}{16} to get -3.

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

Use the distributive property to multiply -2 by x^{2}+\frac{1}{2}x-3.

$$-2x^{2}-x+6$$