Solve 2x^2 11x-21

Question

Simplify the expression

22 x^{3} - 21

Evaluate

2 x^{2} \times 11 x - 21

Solution

More Steps

Evaluate

2 x^{2} \times 11 x

Multiply the terms

22 x^{2} \times x

Multiply the terms with the same base by adding their exponents

22 x^{2 + 1}

Add the numbers

22 x^{3}

22 x^{3} - 21

Show Solution

x = \frac{3 10164}{22}

Alternative Form

x \approx 0.984613

Evaluate

2 x^{2} \times 11 x - 21

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

2 x^{2} \times 11 x - 21 = 0

Multiply

More Steps

Multiply the terms

2 x^{2} \times 11 x

Multiply the terms

22 x^{2} \times x

Multiply the terms with the same base by adding their exponents

22 x^{2 + 1}

Add the numbers

22 x^{3}

22 x^{3} - 21 = 0

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

22 x^{3} = 0 + 21

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

22 x^{3} = 21

Divide both sides

\frac{22 x ^{3}}{22} = \frac{21}{22}

Divide the numbers

x^{3} = \frac{21}{22}

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

3 x^{3} = 3 \frac{21}{22}

Calculate

x = 3 \frac{21}{22}

Solution

More Steps

Evaluate

3 \frac{21}{22}

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

\frac{3 21}{3 22}

Multiply by the Conjugate

\frac{3 21 \times 3 2 2 ^{2}}{3 22 \times 3 2 2 ^{2}}

Simplify

\frac{3 21 \times 3 484}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3484

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

3 21 \times 484

Calculate the product

310164

\frac{3 10164}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

322 \times 3 2 2^{2}

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

3 22 \times 2 2^{2}

Calculate the product

3 2 2^{3}

Reduce the index of the radical and exponent with 3

22

\frac{3 10164}{22}

x = \frac{3 10164}{22}

Alternative Form

x \approx 0.984613

Show Solution