Solve v^2 2v-47=0

Question

Solve the equation

v = \frac{3 188}{2}

Alternative Form

v \approx 2.864327

Evaluate

v^{2} \times 2 v - 47 = 0

Multiply

More Steps

Evaluate

v^{2} \times 2 v

Multiply the terms with the same base by adding their exponents

v^{2 + 1} \times 2

Add the numbers

v^{3} \times 2

Use the commutative property to reorder the terms

2 v^{3}

2 v^{3} - 47 = 0

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

2 v^{3} = 0 + 47

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

2 v^{3} = 47

Divide both sides

\frac{2 v ^{3}}{2} = \frac{47}{2}

Divide the numbers

v^{3} = \frac{47}{2}

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

3 v^{3} = 3 \frac{47}{2}

Calculate

v = 3 \frac{47}{2}

Solution

More Steps

Evaluate

3 \frac{47}{2}

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

\frac{3 47}{3 2}

Multiply by the Conjugate

\frac{3 47 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 47 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

347 \times 34

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

3 47 \times 4

Calculate the product

3188

\frac{3 188}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 188}{2}

v = \frac{3 188}{2}

Alternative Form

v \approx 2.864327

Show Solution