Algebra Examples

$5 v^{2} + 17 v + 5 = 6 v$

Step 1

Move all terms containing $v$ to the left side of the equation.

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Step 1.1

Subtract $6 v$ from both sides of the equation.

$5 v^{2} + 17 v + 5 - 6 v = 0$

Step 1.2

Subtract $6 v$ from $17 v$ .

$5 v^{2} + 11 v + 5 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 5$ , $b = 11$ , and $c = 5$ into the quadratic formula and solve for $v$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (5 \cdot 5)}}{2 \cdot 5}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $11$ to the power of $2$ .

$v = \frac{- 11 \pm \sqrt{121 - 4 \cdot 5 \cdot 5}}{2 \cdot 5}$

Step 4.1.2

Multiply $- 4 \cdot 5 \cdot 5$ .

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Step 4.1.2.1

Multiply $- 4$ by $5$ .

$v = \frac{- 11 \pm \sqrt{121 - 20 \cdot 5}}{2 \cdot 5}$

Step 4.1.2.2

Multiply $- 20$ by $5$ .

$v = \frac{- 11 \pm \sqrt{121 - 100}}{2 \cdot 5}$

Step 4.1.3

Subtract $100$ from $121$ .

$v = \frac{- 11 \pm \sqrt{21}}{2 \cdot 5}$

Step 4.2

Multiply $2$ by $5$ .

$v = \frac{- 11 \pm \sqrt{21}}{10}$

Step 5

The final answer is the combination of both solutions.

$v = - \frac{11 - \sqrt{21}}{10}, - \frac{11 + \sqrt{21}}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{11 - \sqrt{21}}{10}, - \frac{11 + \sqrt{21}}{10}$

Decimal Form:

$v = - 0.64174243 \dots, - 1.55825756 \dots$