Solve x+1/4+2x^2-4x-6/2

$$\frac { x + 1 } { 4 } + \frac { 2 x ^ { 2 } - 4 x - 6 } { 2 }$$

Evaluate

$$x^{2}-\frac{7x}{4}-\frac{11}{4}$$

Short Solution Steps

Divide each term of 2x^{2}-4x-6 by 2 to get -3-2x+x^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -3-2x+x^{2} times \frac{4}{4}.

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

Since \frac{x+1}{4} and \frac{4\left(-3-2x+x^{2}\right)}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x+1+4\left(-3-2x+x^{2}\right).

$$\frac{x+1-12-8x+4x^{2}}{4}$$

Combine like terms in x+1-12-8x+4x^{2}.

$$\frac{-7x-11+4x^{2}}{4}$$

Expand

$$x^{2}-\frac{7x}{4}-\frac{11}{4}$$

Short Solution Steps

Divide each term of 2x^{2}-4x-6 by 2 to get -3-2x+x^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -3-2x+x^{2} times \frac{4}{4}.

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

Since \frac{x+1}{4} and \frac{4\left(-3-2x+x^{2}\right)}{4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x+1+4\left(-3-2x+x^{2}\right).

$$\frac{x+1-12-8x+4x^{2}}{4}$$

Combine like terms in x+1-12-8x+4x^{2}.

$$\frac{-7x-11+4x^{2}}{4}$$