Solve x^3-7x^214x-42

Question

Simplify the expression

- 97 x^{3} - 42

Evaluate

x^{3} - 7 x^{2} \times 14 x - 42

Multiply

More Steps

Multiply the terms

- 7 x^{2} \times 14 x

Multiply the terms

- 98 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 98 x^{2 + 1}

Add the numbers

- 98 x^{3}

x^{3} - 98 x^{3} - 42

Solution

More Steps

Evaluate

x^{3} - 98 x^{3}

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

(1 - 98) x^{3}

Subtract the numbers

- 97 x^{3}

- 97 x^{3} - 42

Show Solution

Find the roots

x = - \frac{3 395178}{97}

Alternative Form

x \approx - 0.756529

Evaluate

x^{3} - 7 x^{2} \times 14 x - 42

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

x^{3} - 7 x^{2} \times 14 x - 42 = 0

Multiply

More Steps

Multiply the terms

7 x^{2} \times 14 x

Multiply the terms

98 x^{2} \times x

Multiply the terms with the same base by adding their exponents

98 x^{2 + 1}

Add the numbers

98 x^{3}

x^{3} - 98 x^{3} - 42 = 0

Subtract the terms

More Steps

Simplify

x^{3} - 98 x^{3}

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

(1 - 98) x^{3}

Subtract the numbers

- 97 x^{3}

- 97 x^{3} - 42 = 0

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

- 97 x^{3} = 0 + 42

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

- 97 x^{3} = 42

Change the signs on both sides of the equation

97 x^{3} = - 42

Divide both sides

\frac{97 x ^{3}}{97} = \frac{- 42}{97}

Divide the numbers

x^{3} = \frac{- 42}{97}

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

x^{3} = - \frac{42}{97}

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

3 x^{3} = 3 - \frac{42}{97}

Calculate

x = 3 - \frac{42}{97}

Solution

More Steps

Evaluate

3 - \frac{42}{97}

An odd root of a negative radicand is always a negative

- 3 \frac{42}{97}

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

- \frac{3 42}{3 97}

Multiply by the Conjugate

\frac{- 3 42 \times 3 9 7 ^{2}}{3 97 \times 3 9 7 ^{2}}

Simplify

\frac{- 3 42 \times 3 9409}{3 97 \times 3 9 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 342 \times 39409

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

- 3 42 \times 9409

Calculate the product

- 3395178

\frac{- 3 395178}{3 97 \times 3 9 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

397 \times 3 9 7^{2}

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

3 97 \times 9 7^{2}

Calculate the product

3 9 7^{3}

Reduce the index of the radical and exponent with 3

97

\frac{- 3 395178}{97}

Calculate

- \frac{3 395178}{97}

x = - \frac{3 395178}{97}

Alternative Form

x \approx - 0.756529

Show Solution