Solve 1+2*(-1+3/2)+{left(3/2right)}^2

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

Evaluate

$$\frac{17}{4}=4.25$$

Solution Steps

Convert -1 to fraction -\frac{2}{2}.

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

Since -\frac{2}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

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

Add -2 and 3 to get 1.

$$1+2\times \frac{1}{2}+\left(\frac{3}{2}\right)^{2}$$

Cancel out 2 and 2.

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

Add 1 and 1 to get 2.

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

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$2+\frac{9}{4}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{8}{4}+\frac{9}{4}$$

Since \frac{8}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{8+9}{4}$$

Add 8 and 9 to get 17.

$$\frac{17}{4}$$

Factor

$$\frac{17}{2 ^ {2}} = 4\frac{1}{4} = 4.25$$