Solve y^2 13y-42=0

Question

Solve the equation

y = \frac{3 7098}{13}

Alternative Form

y \approx 1.478321

Evaluate

y^{2} \times 13 y - 42 = 0

Multiply

More Steps

Evaluate

y^{2} \times 13 y

Multiply the terms with the same base by adding their exponents

y^{2 + 1} \times 13

Add the numbers

y^{3} \times 13

Use the commutative property to reorder the terms

13 y^{3}

13 y^{3} - 42 = 0

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

13 y^{3} = 0 + 42

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

13 y^{3} = 42

Divide both sides

\frac{13 y ^{3}}{13} = \frac{42}{13}

Divide the numbers

y^{3} = \frac{42}{13}

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

3 y^{3} = 3 \frac{42}{13}

Calculate

y = 3 \frac{42}{13}

Solution

More Steps

Evaluate

3 \frac{42}{13}

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

\frac{3 42}{3 13}

Multiply by the Conjugate

\frac{3 42 \times 3 1 3 ^{2}}{3 13 \times 3 1 3 ^{2}}

Simplify

\frac{3 42 \times 3 169}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

342 \times 3169

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

3 42 \times 169

Calculate the product

37098

\frac{3 7098}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3 1 3^{2}

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

3 13 \times 1 3^{2}

Calculate the product

3 1 3^{3}

Reduce the index of the radical and exponent with 3

13

\frac{3 7098}{13}

y = \frac{3 7098}{13}

Alternative Form

y \approx 1.478321

Show Solution