Solve -8x^2 80x-190

Question

Simplify the expression

- 640 x^{3} - 190

Evaluate

- 8 x^{2} \times 80 x - 190

Solution

More Steps

Evaluate

- 8 x^{2} \times 80 x

Multiply the terms

- 640 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 640 x^{2 + 1}

Add the numbers

- 640 x^{3}

- 640 x^{3} - 190

Show Solution

Factor the expression

- 10 (64 x^{3} + 19)

Evaluate

- 8 x^{2} \times 80 x - 190

Multiply

More Steps

Evaluate

- 8 x^{2} \times 80 x

Multiply the terms

- 640 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 640 x^{2 + 1}

Add the numbers

- 640 x^{3}

- 640 x^{3} - 190

Solution

- 10 (64 x^{3} + 19)

Show Solution

Find the roots

x = - \frac{3 19}{4}

Alternative Form

x \approx - 0.6671

Evaluate

- 8 x^{2} \times 80 x - 190

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

- 8 x^{2} \times 80 x - 190 = 0

Multiply

More Steps

Multiply the terms

- 8 x^{2} \times 80 x

Multiply the terms

- 640 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 640 x^{2 + 1}

Add the numbers

- 640 x^{3}

- 640 x^{3} - 190 = 0

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

- 640 x^{3} = 0 + 190

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

- 640 x^{3} = 190

Change the signs on both sides of the equation

640 x^{3} = - 190

Divide both sides

\frac{640 x ^{3}}{640} = \frac{- 190}{640}

Divide the numbers

x^{3} = \frac{- 190}{640}

Divide the numbers

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Evaluate

\frac{- 190}{640}

Cancel out the common factor 10

\frac{- 19}{64}

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

- \frac{19}{64}

x^{3} = - \frac{19}{64}

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

3 x^{3} = 3 - \frac{19}{64}

Calculate

x = 3 - \frac{19}{64}

Solution

More Steps

Evaluate

3 - \frac{19}{64}

An odd root of a negative radicand is always a negative

- 3 \frac{19}{64}

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

- \frac{3 19}{3 64}

Simplify the radical expression

More Steps

Evaluate

364

Write the number in exponential form with the base of 4

3 4^{3}

Reduce the index of the radical and exponent with 3

4

- \frac{3 19}{4}

x = - \frac{3 19}{4}

Alternative Form

x \approx - 0.6671

Show Solution