Solve 2x^211x - 13 = 0

Question

Solve the equation

x = \frac{3 6292}{22}

Alternative Form

x \approx 0.839151

Evaluate

2 x^{2} \times 11 x - 13 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 11 x

Multiply the terms

22 x^{2} \times x

Multiply the terms with the same base by adding their exponents

22 x^{2 + 1}

Add the numbers

22 x^{3}

22 x^{3} - 13 = 0

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

22 x^{3} = 0 + 13

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

22 x^{3} = 13

Divide both sides

\frac{22 x ^{3}}{22} = \frac{13}{22}

Divide the numbers

x^{3} = \frac{13}{22}

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

3 x^{3} = 3 \frac{13}{22}

Calculate

x = 3 \frac{13}{22}

Solution

More Steps

Evaluate

3 \frac{13}{22}

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

\frac{3 13}{3 22}

Multiply by the Conjugate

\frac{3 13 \times 3 2 2 ^{2}}{3 22 \times 3 2 2 ^{2}}

Simplify

\frac{3 13 \times 3 484}{3 22 \times 3 2 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3484

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

3 13 \times 484

Calculate the product

36292

\frac{3 6292}{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 6292}{22}

x = \frac{3 6292}{22}

Alternative Form

x \approx 0.839151

Show Solution