Solve 5x^2 20x - 11 = 0

Question

Solve the equation

x = \frac{3 110}{10}

Alternative Form

x \approx 0.479142

Evaluate

5 x^{2} \times 20 x - 11 = 0

Multiply

More Steps

Evaluate

5 x^{2} \times 20 x

Multiply the terms

100 x^{2} \times x

Multiply the terms with the same base by adding their exponents

100 x^{2 + 1}

Add the numbers

100 x^{3}

100 x^{3} - 11 = 0

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

100 x^{3} = 0 + 11

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

100 x^{3} = 11

Divide both sides

\frac{100 x ^{3}}{100} = \frac{11}{100}

Divide the numbers

x^{3} = \frac{11}{100}

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

3 x^{3} = 3 \frac{11}{100}

Calculate

x = 3 \frac{11}{100}

Solution

More Steps

Evaluate

3 \frac{11}{100}

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

\frac{3 11}{3 100}

Multiply by the Conjugate

\frac{3 11 \times 3 10 0 ^{2}}{3 100 \times 3 10 0 ^{2}}

Simplify

\frac{3 11 \times 10 3 10}{3 100 \times 3 10 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

311 \times 10310

Multiply the terms

3110 \times 10

Use the commutative property to reorder the terms

103110

\frac{10 3 110}{3 100 \times 3 10 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

3100 \times 3 10 0^{2}

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

3 100 \times 10 0^{2}

Calculate the product

3 10 0^{3}

Transform the expression

3 1 0^{6}

Reduce the index of the radical and exponent with 3

1 0^{2}

\frac{10 3 110}{1 0 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{10}{1 0 ^{2}}

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

\frac{1}{1 0 ^{2 - 1}}

Subtract the terms

\frac{1}{1 0 ^{1}}

Simplify

\frac{1}{10}

\frac{3 110}{10}

x = \frac{3 110}{10}

Alternative Form

x \approx 0.479142

Show Solution