Solve y^218y - 13 = 0

Question

Solve the equation

y = \frac{3 156}{6}

Alternative Form

y \approx 0.897202

Evaluate

y^{2} \times 18 y - 13 = 0

Multiply

More Steps

Evaluate

y^{2} \times 18 y

Multiply the terms with the same base by adding their exponents

y^{2 + 1} \times 18

Add the numbers

y^{3} \times 18

Use the commutative property to reorder the terms

18 y^{3}

18 y^{3} - 13 = 0

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

18 y^{3} = 0 + 13

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

18 y^{3} = 13

Divide both sides

\frac{18 y ^{3}}{18} = \frac{13}{18}

Divide the numbers

y^{3} = \frac{13}{18}

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

3 y^{3} = 3 \frac{13}{18}

Calculate

y = 3 \frac{13}{18}

Solution

More Steps

Evaluate

3 \frac{13}{18}

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

\frac{3 13}{3 18}

Multiply by the Conjugate

\frac{3 13 \times 3 1 8 ^{2}}{3 18 \times 3 1 8 ^{2}}

Simplify

\frac{3 13 \times 3 3 12}{3 18 \times 3 1 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3312

Multiply the terms

3156 \times 3

Use the commutative property to reorder the terms

33156

\frac{3 3 156}{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 3 156}{18}

Cancel out the common factor 3

\frac{3 156}{6}

y = \frac{3 156}{6}

Alternative Form

y \approx 0.897202

Show Solution