Solve 0=5x^(2) 9x-2

Question

Solve the equation

x = \frac{3 150}{15}

Alternative Form

x \approx 0.35422

Evaluate

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

Multiply

More Steps

Evaluate

5 x^{2} \times 9 x

Multiply the terms

45 x^{2} \times x

Multiply the terms with the same base by adding their exponents

45 x^{2 + 1}

Add the numbers

45 x^{3}

0 = 45 x^{3} - 2

Swap the sides of the equation

45 x^{3} - 2 = 0

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

45 x^{3} = 0 + 2

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

45 x^{3} = 2

Divide both sides

\frac{45 x ^{3}}{45} = \frac{2}{45}

Divide the numbers

x^{3} = \frac{2}{45}

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

3 x^{3} = 3 \frac{2}{45}

Calculate

x = 3 \frac{2}{45}

Solution

More Steps

Evaluate

3 \frac{2}{45}

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

\frac{3 2}{3 45}

Multiply by the Conjugate

\frac{3 2 \times 3 4 5 ^{2}}{3 45 \times 3 4 5 ^{2}}

Simplify

\frac{3 2 \times 3 3 75}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3375

Multiply the terms

3150 \times 3

Use the commutative property to reorder the terms

33150

\frac{3 3 150}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

345 \times 3 4 5^{2}

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

3 45 \times 4 5^{2}

Calculate the product

3 4 5^{3}

Reduce the index of the radical and exponent with 3

45

\frac{3 3 150}{45}

Cancel out the common factor 3

\frac{3 150}{15}

x = \frac{3 150}{15}

Alternative Form

x \approx 0.35422

Show Solution