Solve -1/2(-29/11)^2-3/2(-29/11)+2

$$- \frac { 1 } { 2 } ( - \frac { 29 } { 11 } ) ^ { 2 } - \frac { 3 } { 2 } ( - \frac { 29 } { 11 } ) + 2$$

Evaluate

$$\frac{300}{121}\approx 2.479338843$$

Solution Steps

Calculate -\frac{29}{11} to the power of 2 and get \frac{841}{121}.

$$-\frac{1}{2}\times \frac{841}{121}-\frac{3}{2}\left(-\frac{29}{11}\right)+2$$

Multiply -\frac{1}{2} times \frac{841}{121} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-841}{2\times 121}-\frac{3}{2}\left(-\frac{29}{11}\right)+2$$

Do the multiplications in the fraction \frac{-841}{2\times 121}.

$$\frac{-841}{242}-\frac{3}{2}\left(-\frac{29}{11}\right)+2$$

Fraction \frac{-841}{242} can be rewritten as -\frac{841}{242} by extracting the negative sign.

$$-\frac{841}{242}-\frac{3}{2}\left(-\frac{29}{11}\right)+2$$

Multiply \frac{3}{2} times -\frac{29}{11} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{841}{242}-\frac{3\left(-29\right)}{2\times 11}+2$$

Do the multiplications in the fraction \frac{3\left(-29\right)}{2\times 11}.

$$-\frac{841}{242}-\frac{-87}{22}+2$$

Fraction \frac{-87}{22} can be rewritten as -\frac{87}{22} by extracting the negative sign.

$$-\frac{841}{242}-\left(-\frac{87}{22}\right)+2$$

The opposite of -\frac{87}{22} is \frac{87}{22}.

$$-\frac{841}{242}+\frac{87}{22}+2$$

Least common multiple of 242 and 22 is 242. Convert -\frac{841}{242} and \frac{87}{22} to fractions with denominator 242.

$$-\frac{841}{242}+\frac{957}{242}+2$$

Since -\frac{841}{242} and \frac{957}{242} have the same denominator, add them by adding their numerators.

$$\frac{-841+957}{242}+2$$

Add -841 and 957 to get 116.

$$\frac{116}{242}+2$$

Reduce the fraction \frac{116}{242} to lowest terms by extracting and canceling out 2.

$$\frac{58}{121}+2$$

Convert 2 to fraction \frac{242}{121}.

$$\frac{58}{121}+\frac{242}{121}$$

Since \frac{58}{121} and \frac{242}{121} have the same denominator, add them by adding their numerators.

$$\frac{58+242}{121}$$

Add 58 and 242 to get 300.

$$\frac{300}{121}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5 ^ {2}}{11 ^ {2}} = 2\frac{58}{121} = 2.479338842975207$$