Solve x^2 24x-180

Question

Simplify the expression

24 x^{3} - 180

Evaluate

x^{2} \times 24 x - 180

Solution

More Steps

Evaluate

x^{2} \times 24 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 24

Add the numbers

x^{3} \times 24

Use the commutative property to reorder the terms

24 x^{3}

24 x^{3} - 180

Show Solution

Factor the expression

12 (2 x^{3} - 15)

Evaluate

x^{2} \times 24 x - 180

Multiply

More Steps

Evaluate

x^{2} \times 24 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 24

Add the numbers

x^{3} \times 24

Use the commutative property to reorder the terms

24 x^{3}

24 x^{3} - 180

Solution

12 (2 x^{3} - 15)

Show Solution

Find the roots

x = \frac{3 60}{2}

Alternative Form

x \approx 1.957434

Evaluate

x^{2} \times 24 x - 180

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

x^{2} \times 24 x - 180 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 24 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 24

Add the numbers

x^{3} \times 24

Use the commutative property to reorder the terms

24 x^{3}

24 x^{3} - 180 = 0

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

24 x^{3} = 0 + 180

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

24 x^{3} = 180

Divide both sides

\frac{24 x ^{3}}{24} = \frac{180}{24}

Divide the numbers

x^{3} = \frac{180}{24}

Cancel out the common factor 12

x^{3} = \frac{15}{2}

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

3 x^{3} = 3 \frac{15}{2}

Calculate

x = 3 \frac{15}{2}

Solution

More Steps

Evaluate

3 \frac{15}{2}

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

\frac{3 15}{3 2}

Multiply by the Conjugate

\frac{3 15 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 15 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 34

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

3 15 \times 4

Calculate the product

360

\frac{3 60}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 60}{2}

x = \frac{3 60}{2}

Alternative Form

x \approx 1.957434

Show Solution