How do you solve $v^{2} - 6 v = 35$ $v^ { 2} - 6v = 35$ by completing the square?

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How do you solve $v^{2} - 6 v = 35$ $v^ { 2} - 6v = 35$ by completing the square?

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Answer 1 · 2017-04-17T17:31:52

By completing the square, we see that

$v^{2} - 6 v - 35 = v^{2} - 6 v + 9 - 44 = {(v - 3)}^{2} - 44$ $v^2-6v-35=v^2-6v+9-44=(v-3)^2-44$

so in order to solve it we can solve

${(v - 3)}^{2} = 44$ $(v-3)^2=44$

By setting $x = v - 3$ $x=v-3$ , we can solve $x^{2} = 44 \Rightarrow x = 2 \pm \sqrt{11}$ $x^2=44 Rightarrow x=2pm sqrt(11)$ , hence $v - 3 = \sqrt{11} \Rightarrow v = 3 + \sqrt{11}$ $v-3=sqrt(11) Rightarrow v=3+sqrt 11$

Answer 2 · 2017-04-17T17:35:15

$v = 2 \sqrt{11} + 3$ $v=2sqrt(11)+3$

Explanation:

Completing the square is a process where one would manipulate the polynomial such that it could be factored into the form (variable +/- number) squared.

The trick to finding the third term in the polynomial is ${(\frac{b}{2})}^{2}$ $(b/2)^2$ . Thus, for this equation, we want the left side to be $v^{2} - 6 v + 9$ $v^2-6v+9$ .

With that in mind, we add 9 to both sides, and simplify.
$v^{2} - 6 v + 9 = 44$ $v^2-6v+9=44$
${(v - 3)}^{2} = 44$ $(v-3)^2=44$

Now we can take the square root of both sides, and solve for v.
$v - 3 = \sqrt{44}$ $v-3=sqrt(44)$
$v = \sqrt{44} + 3$ $v=sqrt(44)+3$
$v = 2 \sqrt{11} + 3$ $v=2sqrt(11)+3$

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How do you solve $v^{2} - 6 v = 35$ $v^ { 2} - 6v = 35$ by completing the square?

2 Answers

Explanation:

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