Solve x^(2) 4x-21

Question

Simplify the expression

4 x^{3} - 21

Evaluate

x^{2} \times 4 x - 21

Solution

More Steps

Evaluate

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 21

Show Solution

Find the roots

x = \frac{3 42}{2}

Alternative Form

x \approx 1.738013

Evaluate

x^{2} \times 4 x - 21

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

x^{2} \times 4 x - 21 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 21 = 0

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

4 x^{3} = 0 + 21

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

4 x^{3} = 21

Divide both sides

\frac{4 x ^{3}}{4} = \frac{21}{4}

Divide the numbers

x^{3} = \frac{21}{4}

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

3 x^{3} = 3 \frac{21}{4}

Calculate

x = 3 \frac{21}{4}

Solution

More Steps

Evaluate

3 \frac{21}{4}

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

\frac{3 21}{3 4}

Multiply by the Conjugate

\frac{3 21 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{3 21 \times 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 232

Multiply the terms

342 \times 2

Use the commutative property to reorder the terms

2342

\frac{2 3 42}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 42}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 42}{2}

x = \frac{3 42}{2}

Alternative Form

x \approx 1.738013

Show Solution