Solve -4x^(2) 45x-40=0

Question

Solve the equation

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

Alternative Form

x \approx - 0.605707

Evaluate

- 4 x^{2} \times 45 x - 40 = 0

Multiply

More Steps

Evaluate

- 4 x^{2} \times 45 x

Multiply the terms

- 180 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 180 x^{2 + 1}

Add the numbers

- 180 x^{3}

- 180 x^{3} - 40 = 0

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

- 180 x^{3} = 0 + 40

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

- 180 x^{3} = 40

Change the signs on both sides of the equation

180 x^{3} = - 40

Divide both sides

\frac{180 x ^{3}}{180} = \frac{- 40}{180}

Divide the numbers

x^{3} = \frac{- 40}{180}

Divide the numbers

More Steps

Evaluate

\frac{- 40}{180}

Cancel out the common factor 20

\frac{- 2}{9}

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

- \frac{2}{9}

x^{3} = - \frac{2}{9}

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

3 x^{3} = 3 - \frac{2}{9}

Calculate

x = 3 - \frac{2}{9}

Solution

More Steps

Evaluate

3 - \frac{2}{9}

An odd root of a negative radicand is always a negative

- 3 \frac{2}{9}

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

- \frac{3 2}{3 9}

Multiply by the Conjugate

\frac{- 3 2 \times 3 9 ^{2}}{3 9 \times 3 9 ^{2}}

Simplify

\frac{- 3 2 \times 3 3 3}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 32 \times 333

Multiply the terms

- 36 \times 3

Use the commutative property to reorder the terms

- 336

\frac{- 3 3 6}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 3 9^{2}

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

3 9 \times 9^{2}

Calculate the product

3 9^{3}

Transform the expression

3 3^{6}

Reduce the index of the radical and exponent with 3

3^{2}

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

Reduce the fraction

More Steps

Evaluate

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

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{- 1}{3 ^{2 - 1}}

Subtract the terms

\frac{- 1}{3 ^{1}}

Simplify

\frac{- 1}{3}

\frac{- 3 6}{3}

Calculate

- \frac{3 6}{3}

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

Alternative Form

x \approx - 0.605707

Show Solution