Solve x^3 4x^2 - 5

Question

Simplify the expression

4 x^{5} - 5

Evaluate

x^{3} \times 4 x^{2} - 5

Solution

More Steps

Evaluate

x^{3} \times 4 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 4

Add the numbers

x^{5} \times 4

Use the commutative property to reorder the terms

4 x^{5}

4 x^{5} - 5

Show Solution

Find the roots

x = \frac{5 40}{2}

Alternative Form

x \approx 1.04564

Evaluate

x^{3} \times 4 x^{2} - 5

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

x^{3} \times 4 x^{2} - 5 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 4 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 4

Add the numbers

x^{5} \times 4

Use the commutative property to reorder the terms

4 x^{5}

4 x^{5} - 5 = 0

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

4 x^{5} = 0 + 5

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

4 x^{5} = 5

Divide both sides

\frac{4 x ^{5}}{4} = \frac{5}{4}

Divide the numbers

x^{5} = \frac{5}{4}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{5}{4}

Calculate

x = 5 \frac{5}{4}

Solution

More Steps

Evaluate

5 \frac{5}{4}

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

\frac{5 5}{5 4}

Multiply by the Conjugate

\frac{5 5 \times 5 4 ^{4}}{5 4 \times 5 4 ^{4}}

Simplify

\frac{5 5 \times 2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

55 \times 258

Multiply the terms

540 \times 2

Use the commutative property to reorder the terms

2540

\frac{2 5 40}{5 4 \times 5 4 ^{4}}

Multiply the numbers

More Steps

Evaluate

54 \times 5 4^{4}

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

5 4 \times 4^{4}

Calculate the product

5 4^{5}

Transform the expression

5 2^{10}

Reduce the index of the radical and exponent with 5

2^{2}

\frac{2 5 40}{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{5 40}{2}

x = \frac{5 40}{2}

Alternative Form

x \approx 1.04564

Show Solution