Solve -2x^2 21x-49=0

Question

Solve the equation

x = - \frac{3 252}{6}

Alternative Form

x \approx - 1.052727

Evaluate

- 2 x^{2} \times 21 x - 49 = 0

Multiply

More Steps

Evaluate

- 2 x^{2} \times 21 x

Multiply the terms

- 42 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 42 x^{2 + 1}

Add the numbers

- 42 x^{3}

- 42 x^{3} - 49 = 0

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

- 42 x^{3} = 0 + 49

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

- 42 x^{3} = 49

Change the signs on both sides of the equation

42 x^{3} = - 49

Divide both sides

\frac{42 x ^{3}}{42} = \frac{- 49}{42}

Divide the numbers

x^{3} = \frac{- 49}{42}

Divide the numbers

More Steps

Evaluate

\frac{- 49}{42}

Cancel out the common factor 7

\frac{- 7}{6}

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

- \frac{7}{6}

x^{3} = - \frac{7}{6}

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

3 x^{3} = 3 - \frac{7}{6}

Calculate

x = 3 - \frac{7}{6}

Solution

More Steps

Evaluate

3 - \frac{7}{6}

An odd root of a negative radicand is always a negative

- 3 \frac{7}{6}

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

- \frac{3 7}{3 6}

Multiply by the Conjugate

\frac{- 3 7 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{- 3 7 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 37 \times 336

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

- 3 7 \times 36

Calculate the product

- 3252

\frac{- 3 252}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3 6^{2}

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

3 6 \times 6^{2}

Calculate the product

3 6^{3}

Reduce the index of the radical and exponent with 3

6

\frac{- 3 252}{6}

Calculate

- \frac{3 252}{6}

x = - \frac{3 252}{6}

Alternative Form

x \approx - 1.052727

Show Solution