Solve 0 = -3x^2 19x-7

Question

Solve the equation

x = - \frac{3 22743}{57}

Alternative Form

x \approx - 0.497059

Evaluate

0 = - 3 x^{2} \times 19 x - 7

Multiply

More Steps

Evaluate

- 3 x^{2} \times 19 x

Multiply the terms

- 57 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 57 x^{2 + 1}

Add the numbers

- 57 x^{3}

0 = - 57 x^{3} - 7

Swap the sides of the equation

- 57 x^{3} - 7 = 0

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

- 57 x^{3} = 0 + 7

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

- 57 x^{3} = 7

Change the signs on both sides of the equation

57 x^{3} = - 7

Divide both sides

\frac{57 x ^{3}}{57} = \frac{- 7}{57}

Divide the numbers

x^{3} = \frac{- 7}{57}

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

x^{3} = - \frac{7}{57}

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

3 x^{3} = 3 - \frac{7}{57}

Calculate

x = 3 - \frac{7}{57}

Solution

More Steps

Evaluate

3 - \frac{7}{57}

An odd root of a negative radicand is always a negative

- 3 \frac{7}{57}

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

- \frac{3 7}{3 57}

Multiply by the Conjugate

\frac{- 3 7 \times 3 5 7 ^{2}}{3 57 \times 3 5 7 ^{2}}

Simplify

\frac{- 3 7 \times 3 3249}{3 57 \times 3 5 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 37 \times 33249

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

- 3 7 \times 3249

Calculate the product

- 322743

\frac{- 3 22743}{3 57 \times 3 5 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

357 \times 3 5 7^{2}

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

3 57 \times 5 7^{2}

Calculate the product

3 5 7^{3}

Reduce the index of the radical and exponent with 3

57

\frac{- 3 22743}{57}

Calculate

- \frac{3 22743}{57}

x = - \frac{3 22743}{57}

Alternative Form

x \approx - 0.497059

Show Solution