Solve for v 59.8=1/20v^2+v

$59.8 = \frac{1}{20} v^{2} + v$

Rewrite the equation as $\frac{1}{20} v^{2} + v = 59.8$ .

$\frac{1}{20} v^{2} + v = 59.8$

Combine $\frac{1}{20}$ and $v^{2}$ .

$\frac{v^{2}}{20} + v = 59.8$

Multiply each term in $\frac{v^{2}}{20} + v = 59.8$ by $20$ to eliminate the fractions.

Multiply each term in $\frac{v^{2}}{20} + v = 59.8$ by $20$ .

$\frac{v^{2}}{20} \cdot 20 + v \cdot 20 = 59.8 \cdot 20$

Simplify the left side.

Simplify each term.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{v^{2}}{20} \cdot 20 + v \cdot 20 = 59.8 \cdot 20$

Rewrite the expression.

$v^{2} + v \cdot 20 = 59.8 \cdot 20$

Move $20$ to the left of $v$ .

$v^{2} + 20 v = 59.8 \cdot 20$

Simplify the right side.

Multiply $59.8$ by $20$ .

$v^{2} + 20 v = 1196$

Subtract $1196$ from both sides of the equation.

$v^{2} + 20 v - 1196 = 0$

Factor $v^{2} + 20 v - 1196$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 1196$ and whose sum is $20$ .

$- 26, 46$

Write the factored form using these integers.

$(v - 26) (v + 46) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$v - 26 = 0$

$v + 46 = 0$

Set $v - 26$ equal to $0$ and solve for $v$ .

Set $v - 26$ equal to $0$ .

$v - 26 = 0$

Add $26$ to both sides of the equation.

$v = 26$

Set $v + 46$ equal to $0$ and solve for $v$ .

Set $v + 46$ equal to $0$ .

$v + 46 = 0$

Subtract $46$ from both sides of the equation.

$v = - 46$

The final solution is all the values that make $(v - 26) (v + 46) = 0$ true.

$v = 26, - 46$

Solve for v 59.8=1/20v^2+v

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