Solve m^3 - 8m^2 11m -10

Question

Simplify the expression

- 87 m^{3} - 10

Evaluate

m^{3} - 8 m^{2} \times 11 m - 10

Multiply

More Steps

Multiply the terms

- 8 m^{2} \times 11 m

Multiply the terms

- 88 m^{2} \times m

Multiply the terms with the same base by adding their exponents

- 88 m^{2 + 1}

Add the numbers

- 88 m^{3}

m^{3} - 88 m^{3} - 10

Solution

More Steps

Evaluate

m^{3} - 88 m^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 88) m^{3}

Subtract the numbers

- 87 m^{3}

- 87 m^{3} - 10

Show Solution

Find the roots

m = - \frac{3 75690}{87}

Alternative Form

m \approx - 0.486213

Evaluate

m^{3} - 8 m^{2} \times 11 m - 10

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

m^{3} - 8 m^{2} \times 11 m - 10 = 0

Multiply

More Steps

Multiply the terms

8 m^{2} \times 11 m

Multiply the terms

88 m^{2} \times m

Multiply the terms with the same base by adding their exponents

88 m^{2 + 1}

Add the numbers

88 m^{3}

m^{3} - 88 m^{3} - 10 = 0

Subtract the terms

More Steps

Simplify

m^{3} - 88 m^{3}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 88) m^{3}

Subtract the numbers

- 87 m^{3}

- 87 m^{3} - 10 = 0

Move the constant to the right-hand side and change its sign

- 87 m^{3} = 0 + 10

Removing 0 doesn't change the value,so remove it from the expression

- 87 m^{3} = 10

Change the signs on both sides of the equation

87 m^{3} = - 10

Divide both sides

\frac{87 m ^{3}}{87} = \frac{- 10}{87}

Divide the numbers

m^{3} = \frac{- 10}{87}

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

m^{3} = - \frac{10}{87}

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

3 m^{3} = 3 - \frac{10}{87}

Calculate

m = 3 - \frac{10}{87}

Solution

More Steps

Evaluate

3 - \frac{10}{87}

An odd root of a negative radicand is always a negative

- 3 \frac{10}{87}

To take a root of a fraction,take the root of the numerator and denominator separately

- \frac{3 10}{3 87}

Multiply by the Conjugate

\frac{- 3 10 \times 3 8 7 ^{2}}{3 87 \times 3 8 7 ^{2}}

Simplify

\frac{- 3 10 \times 3 7569}{3 87 \times 3 8 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 310 \times 37569

The product of roots with the same index is equal to the root of the product

- 3 10 \times 7569

Calculate the product

- 375690

\frac{- 3 75690}{3 87 \times 3 8 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

387 \times 3 8 7^{2}

The product of roots with the same index is equal to the root of the product

3 87 \times 8 7^{2}

Calculate the product

3 8 7^{3}

Reduce the index of the radical and exponent with 3

87

\frac{- 3 75690}{87}

Calculate

- \frac{3 75690}{87}

m = - \frac{3 75690}{87}

Alternative Form

m \approx - 0.486213

Show Solution