Solve f(x)=x^2/2+4x+13

$$f ( x ) = \frac { x ^ { 2 } } { 2 } + 4 x + 13$$

Evaluate

$$\frac{x^{2}}{2}+4x+13$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x+13 times \frac{2}{2}.

$$\frac{x^{2}}{2}+\frac{2\left(4x+13\right)}{2}$$

Since \frac{x^{2}}{2} and \frac{2\left(4x+13\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+2\left(4x+13\right)}{2}$$

Do the multiplications in x^{2}+2\left(4x+13\right).

$$\frac{x^{2}+8x+26}{2}$$

Factor

$$\frac{x^{2}+8x+26}{2}$$

Solution Steps

Factor out \frac{1}{2}. Polynomial x^{2}+8x+26 is not factored since it does not have any rational roots.

$$\frac{x^{2}+8x+26}{2}$$