Solve 4v^210-6 - ScanMath

Question

Simplify the expression

40 v^{2} - 6

Evaluate

4 v^{2} \times 10 - 6

Solution

40 v^{2} - 6

Show Solution

2 (20 v^{2} - 3)

Evaluate

4 v^{2} \times 10 - 6

Multiply the terms

40 v^{2} - 6

Solution

2 (20 v^{2} - 3)

Show Solution

v_{1} = - \frac{15}{10}, v_{2} = \frac{15}{10}

Alternative Form

v_{1} \approx - 0.387298, v_{2} \approx 0.387298

Evaluate

4 v^{2} \times 10 - 6

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

4 v^{2} \times 10 - 6 = 0

Multiply the terms

40 v^{2} - 6 = 0

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

40 v^{2} = 0 + 6

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

40 v^{2} = 6

Divide both sides

\frac{40 v ^{2}}{40} = \frac{6}{40}

Divide the numbers

v^{2} = \frac{6}{40}

Cancel out the common factor 2

v^{2} = \frac{3}{20}

Take the root of both sides of the equation and remember to use both positive and negative roots

v = \pm \frac{3}{20}

Simplify the expression

More Steps

Evaluate

\frac{3}{20}

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

\frac{3}{20}

Simplify the radical expression

More Steps

Evaluate

20

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

The root of a product is equal to the product of the roots of each factor

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

\frac{3}{2 5}

Multiply by the Conjugate

\frac{3 \times 5}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

3 \times 5

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

3 \times 5

Calculate the product

15

\frac{15}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

25 \times 5

When a square root of an expression is multiplied by itself,the result is that expression

2 \times 5

Multiply the terms

10

\frac{15}{10}

v = \pm \frac{15}{10}

Separate the equation into 2 possible cases

v = \frac{15}{10} v = - \frac{15}{10}

Solution

v_{1} = - \frac{15}{10}, v_{2} = \frac{15}{10}

Alternative Form

v_{1} \approx - 0.387298, v_{2} \approx 0.387298

Show Solution