Solve 2v^2 7v-4 - ScanMath

Question

Simplify the expression

14 v^{3} - 4

Evaluate

2 v^{2} \times 7 v - 4

Solution

More Steps

Evaluate

2 v^{2} \times 7 v

Multiply the terms

14 v^{2} \times v

Multiply the terms with the same base by adding their exponents

14 v^{2 + 1}

Add the numbers

14 v^{3}

14 v^{3} - 4

Show Solution

Factor the expression

2 (7 v^{3} - 2)

Evaluate

2 v^{2} \times 7 v - 4

Multiply

More Steps

Evaluate

2 v^{2} \times 7 v

Multiply the terms

14 v^{2} \times v

Multiply the terms with the same base by adding their exponents

14 v^{2 + 1}

Add the numbers

14 v^{3}

14 v^{3} - 4

Solution

2 (7 v^{3} - 2)

Show Solution

Find the roots

v = \frac{3 98}{7}

Alternative Form

v \approx 0.658634

Evaluate

2 v^{2} \times 7 v - 4

To find the roots of the expression,set the expression equal to 0

2 v^{2} \times 7 v - 4 = 0

Multiply

More Steps

Multiply the terms

2 v^{2} \times 7 v

Multiply the terms

14 v^{2} \times v

Multiply the terms with the same base by adding their exponents

14 v^{2 + 1}

Add the numbers

14 v^{3}

14 v^{3} - 4 = 0

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

14 v^{3} = 0 + 4

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

14 v^{3} = 4

Divide both sides

\frac{14 v ^{3}}{14} = \frac{4}{14}

Divide the numbers

v^{3} = \frac{4}{14}

Cancel out the common factor 2

v^{3} = \frac{2}{7}

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

3 v^{3} = 3 \frac{2}{7}

Calculate

v = 3 \frac{2}{7}

Solution

More Steps

Evaluate

3 \frac{2}{7}

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

\frac{3 2}{3 7}

Multiply by the Conjugate

\frac{3 2 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 2 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 349

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

3 2 \times 49

Calculate the product

398

\frac{3 98}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 98}{7}

v = \frac{3 98}{7}

Alternative Form

v \approx 0.658634

Show Solution