Solve -7x^2 3x-3=0

Question

Solve the equation

x = - \frac{3 49}{7}

Alternative Form

x \approx - 0.522758

Evaluate

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

Multiply

More Steps

Evaluate

- 7 x^{2} \times 3 x

Multiply the terms

- 21 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 21 x^{2 + 1}

Add the numbers

- 21 x^{3}

- 21 x^{3} - 3 = 0

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

- 21 x^{3} = 0 + 3

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

- 21 x^{3} = 3

Change the signs on both sides of the equation

21 x^{3} = - 3

Divide both sides

\frac{21 x ^{3}}{21} = \frac{- 3}{21}

Divide the numbers

x^{3} = \frac{- 3}{21}

Divide the numbers

More Steps

Evaluate

\frac{- 3}{21}

Cancel out the common factor 3

\frac{- 1}{7}

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

- \frac{1}{7}

x^{3} = - \frac{1}{7}

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

3 x^{3} = 3 - \frac{1}{7}

Calculate

x = 3 - \frac{1}{7}

Solution

More Steps

Evaluate

3 - \frac{1}{7}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{7}

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

- \frac{3 1}{3 7}

Simplify the radical expression

- \frac{1}{3 7}

Multiply by the Conjugate

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

Simplify

\frac{- 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{- 3 49}{7}

Calculate

- \frac{3 49}{7}

x = - \frac{3 49}{7}

Alternative Form

x \approx - 0.522758

Show Solution