Solve 2x^3-5x^2 3x-7

Question

Simplify the expression

- 13 x^{3} - 7

Evaluate

2 x^{3} - 5 x^{2} \times 3 x - 7

Multiply

More Steps

Multiply the terms

- 5 x^{2} \times 3 x

Multiply the terms

- 15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 15 x^{2 + 1}

Add the numbers

- 15 x^{3}

2 x^{3} - 15 x^{3} - 7

Solution

More Steps

Evaluate

2 x^{3} - 15 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(2 - 15) x^{3}

Subtract the numbers

- 13 x^{3}

- 13 x^{3} - 7

Show Solution

Find the roots

x = - \frac{3 1183}{13}

Alternative Form

x \approx - 0.813551

Evaluate

2 x^{3} - 5 x^{2} \times 3 x - 7

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

2 x^{3} - 5 x^{2} \times 3 x - 7 = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 3 x

Multiply the terms

15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

15 x^{2 + 1}

Add the numbers

15 x^{3}

2 x^{3} - 15 x^{3} - 7 = 0

Subtract the terms

More Steps

Simplify

2 x^{3} - 15 x^{3}

Collect like terms by calculating the sum or difference of their coefficients

(2 - 15) x^{3}

Subtract the numbers

- 13 x^{3}

- 13 x^{3} - 7 = 0

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

- 13 x^{3} = 0 + 7

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

- 13 x^{3} = 7

Change the signs on both sides of the equation

13 x^{3} = - 7

Divide both sides

\frac{13 x ^{3}}{13} = \frac{- 7}{13}

Divide the numbers

x^{3} = \frac{- 7}{13}

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

x^{3} = - \frac{7}{13}

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

3 x^{3} = 3 - \frac{7}{13}

Calculate

x = 3 - \frac{7}{13}

Solution

More Steps

Evaluate

3 - \frac{7}{13}

An odd root of a negative radicand is always a negative

- 3 \frac{7}{13}

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

- \frac{3 7}{3 13}

Multiply by the Conjugate

\frac{- 3 7 \times 3 1 3 ^{2}}{3 13 \times 3 1 3 ^{2}}

Simplify

\frac{- 3 7 \times 3 169}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 37 \times 3169

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

- 3 7 \times 169

Calculate the product

- 31183

\frac{- 3 1183}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3 1 3^{2}

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

3 13 \times 1 3^{2}

Calculate the product

3 1 3^{3}

Reduce the index of the radical and exponent with 3

13

\frac{- 3 1183}{13}

Calculate

- \frac{3 1183}{13}

x = - \frac{3 1183}{13}

Alternative Form

x \approx - 0.813551

Show Solution