Solve (-24r^3-5r^2196r-174)/(8r-9)

Question

Simplify the expression

- \frac{1004 r ^{3} + 174}{8 r - 9}

Show Solution

r = \frac{9}{8}

Show Solution

r = - \frac{3 87 \times 50 2 ^{2}}{502}

Alternative Form

r \approx - 0.557535

Evaluate

\frac{- 24 r ^{3} - 5 r ^{2} \times 196 r - 174}{8 r - 9}

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

\frac{- 24 r ^{3} - 5 r ^{2} \times 196 r - 174}{8 r - 9} = 0

Find the domain

More Steps

\frac{- 24 r ^{3} - 5 r ^{2} \times 196 r - 174}{8 r - 9} = 0, r \neq = \frac{9}{8}

Calculate

\frac{- 24 r ^{3} - 5 r ^{2} \times 196 r - 174}{8 r - 9} = 0

Multiply

More Steps

\frac{- 24 r ^{3} - 980 r ^{3} - 174}{8 r - 9} = 0

Subtract the terms

More Steps

\frac{- 1004 r ^{3} - 174}{8 r - 9} = 0

Cross multiply

- 1004 r^{3} - 174 = (8 r - 9) \times 0

Simplify the equation

- 1004 r^{3} - 174 = 0

Move the constant to the right side

- 1004 r^{3} = 174

Change the signs on both sides of the equation

1004 r^{3} = - 174

Divide both sides

\frac{1004 r ^{3}}{1004} = \frac{- 174}{1004}

Divide the numbers

r^{3} = \frac{- 174}{1004}

Divide the numbers

More Steps

r^{3} = - \frac{87}{502}

Take the 3 -th root on both sides of the equation

3 r^{3} = 3 - \frac{87}{502}

Calculate

r = 3 - \frac{87}{502}

Simplify the root

More Steps

r = - \frac{3 87 \times 50 2 ^{2}}{502}

Check if the solution is in the defined range

r = - \frac{3 87 \times 50 2 ^{2}}{502}, r \neq = \frac{9}{8}

Solution

r = - \frac{3 87 \times 50 2 ^{2}}{502}

Alternative Form

r \approx - 0.557535

Show Solution