Solve (-q^{2} 11q-30)

Question

Simplify the expression

- 11 q^{3} - 30

Evaluate

- q^{2} \times 11 q - 30

Solution

More Steps

Evaluate

- q^{2} \times 11 q

Multiply the terms with the same base by adding their exponents

- q^{2 + 1} \times 11

Add the numbers

- q^{3} \times 11

Use the commutative property to reorder the terms

- 11 q^{3}

- 11 q^{3} - 30

Show Solution

q = - \frac{3 3630}{11}

Alternative Form

q \approx - 1.397149

Evaluate

(- q^{2} \times 11 q - 30)

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

- q^{2} \times 11 q - 30 = 0

Multiply

More Steps

Multiply the terms

q^{2} \times 11 q

Multiply the terms with the same base by adding their exponents

q^{2 + 1} \times 11

Add the numbers

q^{3} \times 11

Use the commutative property to reorder the terms

11 q^{3}

- 11 q^{3} - 30 = 0

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

- 11 q^{3} = 0 + 30

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

- 11 q^{3} = 30

Change the signs on both sides of the equation

11 q^{3} = - 30

Divide both sides

\frac{11 q ^{3}}{11} = \frac{- 30}{11}

Divide the numbers

q^{3} = \frac{- 30}{11}

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

q^{3} = - \frac{30}{11}

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

3 q^{3} = 3 - \frac{30}{11}

Calculate

q = 3 - \frac{30}{11}

Solution

More Steps

Evaluate

3 - \frac{30}{11}

An odd root of a negative radicand is always a negative

- 3 \frac{30}{11}

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

- \frac{3 30}{3 11}

Multiply by the Conjugate

\frac{- 3 30 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{- 3 30 \times 3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 330 \times 3121

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

- 3 30 \times 121

Calculate the product

- 33630

\frac{- 3 3630}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 3 1 1^{2}

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

3 11 \times 1 1^{2}

Calculate the product

3 1 1^{3}

Reduce the index of the radical and exponent with 3

11

\frac{- 3 3630}{11}

Calculate

- \frac{3 3630}{11}

q = - \frac{3 3630}{11}

Alternative Form

q \approx - 1.397149

Show Solution