Solve g(x)=120x+15x^2/2+45/2

$$g ( x ) = 120 x + \frac { 15 x ^ { 2 } } { 2 } + \frac { 45 } { 2 }$$

Evaluate

$$\frac{15\left(x^{2}+16x+3\right)}{2}$$

Short Solution Steps

Since \frac{15x^{2}}{2} and \frac{45}{2} have the same denominator, add them by adding their numerators.

$$120x+\frac{15x^{2}+45}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 120x times \frac{2}{2}.

$$\frac{2\times 120x}{2}+\frac{15x^{2}+45}{2}$$

Since \frac{2\times 120x}{2} and \frac{15x^{2}+45}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\times 120x+15x^{2}+45}{2}$$

Do the multiplications in 2\times 120x+15x^{2}+45.

$$\frac{240x+15x^{2}+45}{2}$$

Factor

$$\frac{15\left(x-\left(-\sqrt{61}-8\right)\right)\left(x-\left(\sqrt{61}-8\right)\right)}{2}$$