Solve 2x+5-x^2+11x/2+15/2

$$2x+5- { x }^{ 2 } + \frac{ 11x }{ 2 } + \frac{ 15 }{ 2 }$$

Evaluate

$$-x^{2}+\frac{15x}{2}+\frac{25}{2}$$

Short Solution Steps

Add 5 and \frac{15}{2} to get \frac{25}{2}.

$$2x+\frac{25}{2}-x^{2}+\frac{11x}{2}$$

Since \frac{25}{2} and \frac{11x}{2} have the same denominator, add them by adding their numerators.

$$2x+\frac{25+11x}{2}-x^{2}$$

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

$$2x+\frac{25+11x}{2}-\frac{2x^{2}}{2}$$

Since \frac{25+11x}{2} and \frac{2x^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$2x+\frac{25+11x-2x^{2}}{2}$$

Divide each term of 25+11x-2x^{2} by 2 to get \frac{25}{2}+\frac{11}{2}x-x^{2}.

$$2x+\frac{25}{2}+\frac{11}{2}x-x^{2}$$

Combine 2x and \frac{11}{2}x to get \frac{15}{2}x.

$$\frac{15}{2}x+\frac{25}{2}-x^{2}$$

Factor

$$-\left(x-\frac{15-5\sqrt{17}}{4}\right)\left(x-\frac{5\sqrt{17}+15}{4}\right)$$