Solve 361-25v^2 - ScanMath

Question

Factor the expression

(19 - 5 v) (19 + 5 v)

Evaluate

361 - 25 v^{2}

Rewrite the expression in exponential form

1 9^{2} - (5 v)^{2}

Solution

(19 - 5 v) (19 + 5 v)

Show Solution

v_{1} = - \frac{19}{5}, v_{2} = \frac{19}{5}

Alternative Form

v_{1} = - 3.8, v_{2} = 3.8

Evaluate

361 - 25 v^{2}

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

361 - 25 v^{2} = 0

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

- 25 v^{2} = 0 - 361

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

- 25 v^{2} = - 361

Change the signs on both sides of the equation

25 v^{2} = 361

Divide both sides

\frac{25 v ^{2}}{25} = \frac{361}{25}

Divide the numbers

v^{2} = \frac{361}{25}

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

v = \pm \frac{361}{25}

Simplify the expression

More Steps

Evaluate

\frac{361}{25}

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

\frac{361}{25}

Simplify the radical expression

More Steps

Evaluate

361

Write the number in exponential form with the base of 19

1 9^{2}

Reduce the index of the radical and exponent with 2

19

\frac{19}{25}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{19}{5}

v = \pm \frac{19}{5}

Separate the equation into 2 possible cases

v = \frac{19}{5} v = - \frac{19}{5}

Solution

v_{1} = - \frac{19}{5}, v_{2} = \frac{19}{5}

Alternative Form

v_{1} = - 3.8, v_{2} = 3.8

Show Solution