Solve -5x^22x-9=0

Question

Solve the equation

x = - \frac{3 900}{10}

Alternative Form

x \approx - 0.965489

Evaluate

- 5 x^{2} \times 2 x - 9 = 0

Multiply

More Steps

Evaluate

- 5 x^{2} \times 2 x

Multiply the terms

- 10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 10 x^{2 + 1}

Add the numbers

- 10 x^{3}

- 10 x^{3} - 9 = 0

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

- 10 x^{3} = 0 + 9

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

- 10 x^{3} = 9

Change the signs on both sides of the equation

10 x^{3} = - 9

Divide both sides

\frac{10 x ^{3}}{10} = \frac{- 9}{10}

Divide the numbers

x^{3} = \frac{- 9}{10}

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

x^{3} = - \frac{9}{10}

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

3 x^{3} = 3 - \frac{9}{10}

Calculate

x = 3 - \frac{9}{10}

Solution

More Steps

Evaluate

3 - \frac{9}{10}

An odd root of a negative radicand is always a negative

- 3 \frac{9}{10}

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

- \frac{3 9}{3 10}

Multiply by the Conjugate

\frac{- 3 9 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{- 3 9 \times 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 39 \times 3100

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

- 3 9 \times 100

Calculate the product

- 3900

\frac{- 3 900}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3 1 0^{2}

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

3 10 \times 1 0^{2}

Calculate the product

3 1 0^{3}

Reduce the index of the radical and exponent with 3

10

\frac{- 3 900}{10}

Calculate

- \frac{3 900}{10}

x = - \frac{3 900}{10}

Alternative Form

x \approx - 0.965489

Show Solution