Solve -5x^2 30x-40

Question

Simplify the expression

- 150 x^{3} - 40

Evaluate

- 5 x^{2} \times 30 x - 40

Solution

More Steps

Evaluate

- 5 x^{2} \times 30 x

Multiply the terms

- 150 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 150 x^{2 + 1}

Add the numbers

- 150 x^{3}

- 150 x^{3} - 40

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Factor the expression

- 10 (15 x^{3} + 4)

Evaluate

- 5 x^{2} \times 30 x - 40

Multiply

More Steps

Evaluate

- 5 x^{2} \times 30 x

Multiply the terms

- 150 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 150 x^{2 + 1}

Add the numbers

- 150 x^{3}

- 150 x^{3} - 40

Solution

- 10 (15 x^{3} + 4)

Show Solution

Find the roots

x = - \frac{3 900}{15}

Alternative Form

x \approx - 0.64366

Evaluate

- 5 x^{2} \times 30 x - 40

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

- 5 x^{2} \times 30 x - 40 = 0

Multiply

More Steps

Multiply the terms

- 5 x^{2} \times 30 x

Multiply the terms

- 150 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 150 x^{2 + 1}

Add the numbers

- 150 x^{3}

- 150 x^{3} - 40 = 0

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

- 150 x^{3} = 0 + 40

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

- 150 x^{3} = 40

Change the signs on both sides of the equation

150 x^{3} = - 40

Divide both sides

\frac{150 x ^{3}}{150} = \frac{- 40}{150}

Divide the numbers

x^{3} = \frac{- 40}{150}

Divide the numbers

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Evaluate

\frac{- 40}{150}

Cancel out the common factor 10

\frac{- 4}{15}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{4}{15}

x^{3} = - \frac{4}{15}

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

3 x^{3} = 3 - \frac{4}{15}

Calculate

x = 3 - \frac{4}{15}

Solution

More Steps

Evaluate

3 - \frac{4}{15}

An odd root of a negative radicand is always a negative

- 3 \frac{4}{15}

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

- \frac{3 4}{3 15}

Multiply by the Conjugate

\frac{- 3 4 \times 3 1 5 ^{2}}{3 15 \times 3 1 5 ^{2}}

Simplify

\frac{- 3 4 \times 3 225}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 34 \times 3225

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

- 3 4 \times 225

Calculate the product

- 3900

\frac{- 3 900}{3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3 1 5^{2}

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

3 15 \times 1 5^{2}

Calculate the product

3 1 5^{3}

Reduce the index of the radical and exponent with 3

15

\frac{- 3 900}{15}

Calculate

- \frac{3 900}{15}

x = - \frac{3 900}{15}

Alternative Form

x \approx - 0.64366

Show Solution