Solve f(x)=3(-1/2)^2-2(-sqrt{2})+5

$$f ( x ) = 3 ( - \frac { 1 } { 2 } ) ^ { 2 } - 2 ( - \sqrt { 2 } ) + 5$$

Evaluate

$$2\sqrt{2}+\frac{23}{4}\approx 8.578427125$$

Solution Steps

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$3\times \frac{1}{4}-2\left(-\sqrt{2}\right)+5$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{3}{4}-2\left(-\sqrt{2}\right)+5$$

Multiply -1 and 2 to get -2.

$$\frac{3}{4}-2\left(-1\right)\sqrt{2}+5$$

Multiply -2 and -1 to get 2.

$$\frac{3}{4}+2\sqrt{2}+5$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{3}{4}+2\sqrt{2}+\frac{20}{4}$$

Since \frac{3}{4} and \frac{20}{4} have the same denominator, add them by adding their numerators.

$$\frac{3+20}{4}+2\sqrt{2}$$

Add 3 and 20 to get 23.

$$\frac{23}{4}+2\sqrt{2}$$

Factor

$$\frac{8 \sqrt{2} + 23}{4} = 8.57842712474619$$