Solve (3{left(-1/4right)}^2+2(-1/4))((-1/4)+6)

$$(3 { \left(- \frac{ 1 }{ 4 } \right) }^{ 2 } +2(- \frac{ 1 }{ 4 } ))((- \frac{ 1 }{ 4 } )+6)$$

Evaluate

$$-\frac{115}{64}=-1.796875$$

Solution Steps

Calculate -\frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\left(3\times \frac{1}{16}+2\left(-\frac{1}{4}\right)\right)\left(-\frac{1}{4}+6\right)$$

Multiply 3 and \frac{1}{16} to get \frac{3}{16}.

$$\left(\frac{3}{16}+2\left(-\frac{1}{4}\right)\right)\left(-\frac{1}{4}+6\right)$$

Express 2\left(-\frac{1}{4}\right) as a single fraction.

$$\left(\frac{3}{16}+\frac{2\left(-1\right)}{4}\right)\left(-\frac{1}{4}+6\right)$$

Multiply 2 and -1 to get -2.

$$\left(\frac{3}{16}+\frac{-2}{4}\right)\left(-\frac{1}{4}+6\right)$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\left(\frac{3}{16}-\frac{1}{2}\right)\left(-\frac{1}{4}+6\right)$$

Least common multiple of 16 and 2 is 16. Convert \frac{3}{16} and \frac{1}{2} to fractions with denominator 16.

$$\left(\frac{3}{16}-\frac{8}{16}\right)\left(-\frac{1}{4}+6\right)$$

Since \frac{3}{16} and \frac{8}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-8}{16}\left(-\frac{1}{4}+6\right)$$

Subtract 8 from 3 to get -5.

$$-\frac{5}{16}\left(-\frac{1}{4}+6\right)$$

Convert 6 to fraction \frac{24}{4}.

$$-\frac{5}{16}\left(-\frac{1}{4}+\frac{24}{4}\right)$$

Since -\frac{1}{4} and \frac{24}{4} have the same denominator, add them by adding their numerators.

$$-\frac{5}{16}\times \frac{-1+24}{4}$$

Add -1 and 24 to get 23.

$$-\frac{5}{16}\times \frac{23}{4}$$

Multiply -\frac{5}{16} times \frac{23}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 23}{16\times 4}$$

Do the multiplications in the fraction \frac{-5\times 23}{16\times 4}.

$$\frac{-115}{64}$$

Fraction \frac{-115}{64} can be rewritten as -\frac{115}{64} by extracting the negative sign.

$$-\frac{115}{64}$$

Factor

$$-\frac{115}{64} = -1\frac{51}{64} = -1.796875$$