Solve -4x^(2) 44x-40=0

Question

Solve the equation

x = - \frac{3 2420}{22}

Alternative Form

x \approx - 0.610261

Evaluate

- 4 x^{2} \times 44 x - 40 = 0

Multiply

More Steps

Evaluate

- 4 x^{2} \times 44 x

Multiply the terms

- 176 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 176 x^{2 + 1}

Add the numbers

- 176 x^{3}

- 176 x^{3} - 40 = 0

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

- 176 x^{3} = 0 + 40

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

- 176 x^{3} = 40

Change the signs on both sides of the equation

176 x^{3} = - 40

Divide both sides

\frac{176 x ^{3}}{176} = \frac{- 40}{176}

Divide the numbers

x^{3} = \frac{- 40}{176}

Divide the numbers

More Steps

Evaluate

\frac{- 40}{176}

Cancel out the common factor 8

\frac{- 5}{22}

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

- \frac{5}{22}

x^{3} = - \frac{5}{22}

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

3 x^{3} = 3 - \frac{5}{22}

Calculate

x = 3 - \frac{5}{22}

Solution

More Steps

Evaluate

3 - \frac{5}{22}

An odd root of a negative radicand is always a negative

- 3 \frac{5}{22}

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

- \frac{3 5}{3 22}

Multiply by the Conjugate

\frac{- 3 5 \times 3 2 2 ^{2}}{3 22 \times 3 2 2 ^{2}}

Simplify

\frac{- 3 5 \times 3 484}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 35 \times 3484

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

- 3 5 \times 484

Calculate the product

- 32420

\frac{- 3 2420}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

322 \times 3 2 2^{2}

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

3 22 \times 2 2^{2}

Calculate the product

3 2 2^{3}

Reduce the index of the radical and exponent with 3

22

\frac{- 3 2420}{22}

Calculate

- \frac{3 2420}{22}

x = - \frac{3 2420}{22}

Alternative Form

x \approx - 0.610261

Show Solution