Solve v^2 6v-59=0

Question

Solve the equation

v = \frac{3 2124}{6}

Alternative Form

v \approx 2.142398

Evaluate

v^{2} \times 6 v - 59 = 0

Multiply

More Steps

Evaluate

v^{2} \times 6 v

Multiply the terms with the same base by adding their exponents

v^{2 + 1} \times 6

Add the numbers

v^{3} \times 6

Use the commutative property to reorder the terms

6 v^{3}

6 v^{3} - 59 = 0

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

6 v^{3} = 0 + 59

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

6 v^{3} = 59

Divide both sides

\frac{6 v ^{3}}{6} = \frac{59}{6}

Divide the numbers

v^{3} = \frac{59}{6}

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

3 v^{3} = 3 \frac{59}{6}

Calculate

v = 3 \frac{59}{6}

Solution

More Steps

Evaluate

3 \frac{59}{6}

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

\frac{3 59}{3 6}

Multiply by the Conjugate

\frac{3 59 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 59 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

359 \times 336

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

3 59 \times 36

Calculate the product

32124

\frac{3 2124}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3 6^{2}

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

3 6 \times 6^{2}

Calculate the product

3 6^{3}

Reduce the index of the radical and exponent with 3

6

\frac{3 2124}{6}

v = \frac{3 2124}{6}

Alternative Form

v \approx 2.142398

Show Solution