Solve (2-r^2)/5-r/2

Evaluate

\frac{2 - r ^{2}}{5} - \frac{r}{2}

To find the roots of the expression,set the expression equal to 0

\frac{2 - r ^{2}}{5} - \frac{r}{2} = 0

Subtract the terms

More Steps

\frac{4 - 2 r ^{2} - 5 r}{10} = 0

Simplify

4 - 2 r^{2} - 5 r = 0

Rewrite in standard form

- 2 r^{2} - 5 r + 4 = 0

Multiply both sides

2 r^{2} + 5 r - 4 = 0

Substitute a= 2,b= 5 and c= - 4 into the quadratic formula r = \frac{- b \pm b ^{2} - 4 a c}{2 a}

r = \frac{- 5 \pm 5 ^{2} - 4 \times 2 ( - 4 )}{2 \times 2}

Simplify the expression

r = \frac{- 5 \pm 5 ^{2} - 4 \times 2 ( - 4 )}{4}

Simplify the expression

More Steps

r = \frac{- 5 \pm 57}{4}

Separate the equation into 2 possible cases

r = \frac{- 5 + 57}{4} r = \frac{- 5 - 57}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

r = \frac{- 5 + 57}{4} r = - \frac{5 + 57}{4}

Solution

r_{1} = - \frac{5 + 57}{4}, r_{2} = \frac{- 5 + 57}{4}

Alternative Form

r_{1} \approx - 3.137459, r_{2} \approx 0.637459

Simplify the expression