Solve 0=-20x^2 37x-15

Question

Solve the equation

x = - \frac{3 8214}{74}

Alternative Form

x \approx - 0.272659

Evaluate

0 = - 20 x^{2} \times 37 x - 15

Multiply

More Steps

Evaluate

- 20 x^{2} \times 37 x

Multiply the terms

- 740 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 740 x^{2 + 1}

Add the numbers

- 740 x^{3}

0 = - 740 x^{3} - 15

Swap the sides of the equation

- 740 x^{3} - 15 = 0

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

- 740 x^{3} = 0 + 15

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

- 740 x^{3} = 15

Change the signs on both sides of the equation

740 x^{3} = - 15

Divide both sides

\frac{740 x ^{3}}{740} = \frac{- 15}{740}

Divide the numbers

x^{3} = \frac{- 15}{740}

Divide the numbers

More Steps

Evaluate

\frac{- 15}{740}

Cancel out the common factor 5

\frac{- 3}{148}

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

- \frac{3}{148}

x^{3} = - \frac{3}{148}

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

3 x^{3} = 3 - \frac{3}{148}

Calculate

x = 3 - \frac{3}{148}

Solution

More Steps

Evaluate

3 - \frac{3}{148}

An odd root of a negative radicand is always a negative

- 3 \frac{3}{148}

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

- \frac{3 3}{3 148}

Multiply by the Conjugate

\frac{- 3 3 \times 3 14 8 ^{2}}{3 148 \times 3 14 8 ^{2}}

Simplify

\frac{- 3 3 \times 2 3 2738}{3 148 \times 3 14 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 33 \times 232738

Multiply the terms

- 38214 \times 2

Use the commutative property to reorder the terms

- 238214

\frac{- 2 3 8214}{3 148 \times 3 14 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

3148 \times 3 14 8^{2}

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

3 148 \times 14 8^{2}

Calculate the product

3 14 8^{3}

Reduce the index of the radical and exponent with 3

148

\frac{- 2 3 8214}{148}

Cancel out the common factor 2

\frac{- 3 8214}{74}

Calculate

- \frac{3 8214}{74}

x = - \frac{3 8214}{74}

Alternative Form

x \approx - 0.272659

Show Solution