Solve 2x^3+245 - ScanMath

Question

Find the roots

x = - \frac{3 980}{2}

Alternative Form

x \approx - 4.966442

Evaluate

2 x^{3} + 245

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

2 x^{3} + 245 = 0

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

2 x^{3} = 0 - 245

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

2 x^{3} = - 245

Divide both sides

\frac{2 x ^{3}}{2} = \frac{- 245}{2}

Divide the numbers

x^{3} = \frac{- 245}{2}

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

x^{3} = - \frac{245}{2}

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

3 x^{3} = 3 - \frac{245}{2}

Calculate

x = 3 - \frac{245}{2}

Solution

More Steps

Evaluate

3 - \frac{245}{2}

An odd root of a negative radicand is always a negative

- 3 \frac{245}{2}

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

- \frac{3 245}{3 2}

Multiply by the Conjugate

\frac{- 3 245 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{- 3 245 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 3245 \times 34

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

- 3 245 \times 4

Calculate the product

- 3980

\frac{- 3 980}{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{- 3 980}{2}

Calculate

- \frac{3 980}{2}

x = - \frac{3 980}{2}

Alternative Form

x \approx - 4.966442

Show Solution