Solve 2x^29x-31=0

Question

Solve the equation

x = \frac{3 372}{6}

Alternative Form

x \approx 1.198661

Evaluate

2 x^{2} \times 9 x - 31 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 9 x

Multiply the terms

18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

18 x^{2 + 1}

Add the numbers

18 x^{3}

18 x^{3} - 31 = 0

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

18 x^{3} = 0 + 31

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

18 x^{3} = 31

Divide both sides

\frac{18 x ^{3}}{18} = \frac{31}{18}

Divide the numbers

x^{3} = \frac{31}{18}

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

3 x^{3} = 3 \frac{31}{18}

Calculate

x = 3 \frac{31}{18}

Solution

More Steps

Evaluate

3 \frac{31}{18}

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

\frac{3 31}{3 18}

Multiply by the Conjugate

\frac{3 31 \times 3 1 8 ^{2}}{3 18 \times 3 1 8 ^{2}}

Simplify

\frac{3 31 \times 3 3 12}{3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

331 \times 3312

Multiply the terms

3372 \times 3

Use the commutative property to reorder the terms

33372

\frac{3 3 372}{3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

318 \times 3 1 8^{2}

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

3 18 \times 1 8^{2}

Calculate the product

3 1 8^{3}

Reduce the index of the radical and exponent with 3

18

\frac{3 3 372}{18}

Cancel out the common factor 3

\frac{3 372}{6}

x = \frac{3 372}{6}

Alternative Form

x \approx 1.198661

Show Solution