Solve x^2 120x-160

Question

Simplify the expression

120 x^{3} - 160

Evaluate

x^{2} \times 120 x - 160

Solution

More Steps

Evaluate

x^{2} \times 120 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 120

Add the numbers

x^{3} \times 120

Use the commutative property to reorder the terms

120 x^{3}

120 x^{3} - 160

Show Solution

Factor the expression

40 (3 x^{3} - 4)

Evaluate

x^{2} \times 120 x - 160

Multiply

More Steps

Evaluate

x^{2} \times 120 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 120

Add the numbers

x^{3} \times 120

Use the commutative property to reorder the terms

120 x^{3}

120 x^{3} - 160

Solution

40 (3 x^{3} - 4)

Show Solution

Find the roots

x = \frac{3 36}{3}

Alternative Form

x \approx 1.100642

Evaluate

x^{2} \times 120 x - 160

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

x^{2} \times 120 x - 160 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 120 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 120

Add the numbers

x^{3} \times 120

Use the commutative property to reorder the terms

120 x^{3}

120 x^{3} - 160 = 0

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

120 x^{3} = 0 + 160

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

120 x^{3} = 160

Divide both sides

\frac{120 x ^{3}}{120} = \frac{160}{120}

Divide the numbers

x^{3} = \frac{160}{120}

Cancel out the common factor 40

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

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

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

Calculate

x = 3 \frac{4}{3}

Solution

More Steps

Evaluate

3 \frac{4}{3}

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

\frac{3 4}{3 3}

Multiply by the Conjugate

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

Simplify

\frac{3 4 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 39

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

3 4 \times 9

Calculate the product

336

\frac{3 36}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 36}{3}

x = \frac{3 36}{3}

Alternative Form

x \approx 1.100642

Show Solution