Solve q^(2) 11q-42

Question

Simplify the expression

11 q^{3} - 42

Evaluate

q^{2} \times 11 q - 42

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} - 42

Show Solution

q = \frac{3 5082}{11}

Alternative Form

q \approx 1.562976

Evaluate

q^{2} \times 11 q - 42

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

q^{2} \times 11 q - 42 = 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} - 42 = 0

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

11 q^{3} = 0 + 42

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

11 q^{3} = 42

Divide both sides

\frac{11 q ^{3}}{11} = \frac{42}{11}

Divide the numbers

q^{3} = \frac{42}{11}

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

3 q^{3} = 3 \frac{42}{11}

Calculate

q = 3 \frac{42}{11}

Solution

More Steps

Evaluate

3 \frac{42}{11}

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

\frac{3 42}{3 11}

Multiply by the Conjugate

\frac{3 42 \times 3 1 1 ^{2}}{3 11 \times 3 1 1 ^{2}}

Simplify

\frac{3 42 \times 3 121}{3 11 \times 3 1 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

342 \times 3121

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

3 42 \times 121

Calculate the product

35082

\frac{3 5082}{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 5082}{11}

q = \frac{3 5082}{11}

Alternative Form

q \approx 1.562976

Show Solution