Solve 9v^2006-39 - ScanMath

Question

Simplify the expression

Solution

54 v^{2} - 39

Evaluate

9 v^{2} \times 6 - 39

Solution

54 v^{2} - 39

Show Solution

Factor the expression

Factor

3 (18 v^{2} - 13)

Evaluate

9 v^{2} \times 6 - 39

Multiply the terms

54 v^{2} - 39

Solution

3 (18 v^{2} - 13)

Show Solution

Find the roots

Find the roots of the algebra expression

v_{1} = - \frac{26}{6}, v_{2} = \frac{26}{6}

Alternative Form

v_{1} \approx - 0.849837, v_{2} \approx 0.849837

Evaluate

9 v^{2} \times 6 - 39

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

9 v^{2} \times 6 - 39 = 0

Multiply the terms

54 v^{2} - 39 = 0

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

54 v^{2} = 0 + 39

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

54 v^{2} = 39

Divide both sides

\frac{54 v ^{2}}{54} = \frac{39}{54}

Divide the numbers

v^{2} = \frac{39}{54}

Cancel out the common factor 3

v^{2} = \frac{13}{18}

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

v = \pm \frac{13}{18}

Simplify the expression

More Steps

Evaluate

\frac{13}{18}

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

\frac{13}{18}

Simplify the radical expression

More Steps

Evaluate

18

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

9 \times 2

Write the number in exponential form with the base of 3

3^{2} \times 2

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

3^{2} \times 2

Reduce the index of the radical and exponent with 2

32

\frac{13}{3 2}

Multiply by the Conjugate

\frac{13 \times 2}{3 2 \times 2}

Multiply the numbers

More Steps

Evaluate

13 \times 2

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

13 \times 2

Calculate the product

26

\frac{26}{3 2 \times 2}

Multiply the numbers

More Steps

Evaluate

32 \times 2

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

3 \times 2

Multiply the terms

6

\frac{26}{6}

v = \pm \frac{26}{6}

Separate the equation into 2 possible cases

v = \frac{26}{6} v = - \frac{26}{6}

Solution

v_{1} = - \frac{26}{6}, v_{2} = \frac{26}{6}

Alternative Form

v_{1} \approx - 0.849837, v_{2} \approx 0.849837

Show Solution

9v^2006 39

Simplify the expression

Factor the expression

Find the roots