Solve -x^2 310x -7400

Question

Simplify the expression

- 310 x^{3} - 7400

Evaluate

- x^{2} \times 310 x - 7400

Solution

More Steps

Evaluate

- x^{2} \times 310 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 310

Add the numbers

- x^{3} \times 310

Use the commutative property to reorder the terms

- 310 x^{3}

- 310 x^{3} - 7400

Show Solution

Factor the expression

- 10 (31 x^{3} + 740)

Evaluate

- x^{2} \times 310 x - 7400

Multiply

More Steps

Evaluate

x^{2} \times 310 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 310

Add the numbers

x^{3} \times 310

Use the commutative property to reorder the terms

310 x^{3}

- 310 x^{3} - 7400

Solution

- 10 (31 x^{3} + 740)

Show Solution

Find the roots

x = - \frac{3 711140}{31}

Alternative Form

x \approx - 2.87932

Evaluate

- x^{2} \times 310 x - 7400

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

- x^{2} \times 310 x - 7400 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 310 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 310

Add the numbers

x^{3} \times 310

Use the commutative property to reorder the terms

310 x^{3}

- 310 x^{3} - 7400 = 0

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

- 310 x^{3} = 0 + 7400

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

- 310 x^{3} = 7400

Change the signs on both sides of the equation

310 x^{3} = - 7400

Divide both sides

\frac{310 x ^{3}}{310} = \frac{- 7400}{310}

Divide the numbers

x^{3} = \frac{- 7400}{310}

Divide the numbers

More Steps

Evaluate

\frac{- 7400}{310}

Cancel out the common factor 10

\frac{- 740}{31}

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

- \frac{740}{31}

x^{3} = - \frac{740}{31}

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

3 x^{3} = 3 - \frac{740}{31}

Calculate

x = 3 - \frac{740}{31}

Solution

More Steps

Evaluate

3 - \frac{740}{31}

An odd root of a negative radicand is always a negative

- 3 \frac{740}{31}

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

- \frac{3 740}{3 31}

Multiply by the Conjugate

\frac{- 3 740 \times 3 3 1 ^{2}}{3 31 \times 3 3 1 ^{2}}

Simplify

\frac{- 3 740 \times 3 961}{3 31 \times 3 3 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 3740 \times 3961

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

- 3 740 \times 961

Calculate the product

- 3711140

\frac{- 3 711140}{3 31 \times 3 3 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

331 \times 3 3 1^{2}

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

3 31 \times 3 1^{2}

Calculate the product

3 3 1^{3}

Reduce the index of the radical and exponent with 3

31

\frac{- 3 711140}{31}

Calculate

- \frac{3 711140}{31}

x = - \frac{3 711140}{31}

Alternative Form

x \approx - 2.87932

Show Solution