Solve y=3(-5/6)^2+5(-5/6)-2

$$y = 3 ( - \frac { 5 } { 6 } ) ^ { 2 } + 5 ( - \frac { 5 } { 6 } ) - 2$$

Solve for y

$$y = -\frac{49}{12} = -4\frac{1}{12} \approx -4.083333333$$

Steps for Solving Linear Equation

Calculate -\frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$y=3\times \frac{25}{36}+5\left(-\frac{5}{6}\right)-2$$

Express 3\times \frac{25}{36} as a single fraction.

$$y=\frac{3\times 25}{36}+5\left(-\frac{5}{6}\right)-2$$

Multiply 3 and 25 to get 75.

$$y=\frac{75}{36}+5\left(-\frac{5}{6}\right)-2$$

Reduce the fraction \frac{75}{36} to lowest terms by extracting and canceling out 3.

$$y=\frac{25}{12}+5\left(-\frac{5}{6}\right)-2$$

Express 5\left(-\frac{5}{6}\right) as a single fraction.

$$y=\frac{25}{12}+\frac{5\left(-5\right)}{6}-2$$

Multiply 5 and -5 to get -25.

$$y=\frac{25}{12}+\frac{-25}{6}-2$$

Fraction \frac{-25}{6} can be rewritten as -\frac{25}{6} by extracting the negative sign.

$$y=\frac{25}{12}-\frac{25}{6}-2$$

Least common multiple of 12 and 6 is 12. Convert \frac{25}{12} and \frac{25}{6} to fractions with denominator 12.

$$y=\frac{25}{12}-\frac{50}{12}-2$$

Since \frac{25}{12} and \frac{50}{12} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{25-50}{12}-2$$

Subtract 50 from 25 to get -25.

$$y=-\frac{25}{12}-2$$

Convert 2 to fraction \frac{24}{12}.

$$y=-\frac{25}{12}-\frac{24}{12}$$

Since -\frac{25}{12} and \frac{24}{12} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{-25-24}{12}$$

Subtract 24 from -25 to get -49.

$$y=-\frac{49}{12}$$

Assign y

$$y≔-\frac{49}{12}$$