How do you solve $v^{2} - 17 v + 200 = 13 v - 43$ $v^2-17v+200=13v-43$ by completing the square?

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How do you solve $v^{2} - 17 v + 200 = 13 v - 43$ $v^2-17v+200=13v-43$ by completing the square?

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Answer 1 · 2017-11-13T11:14:42

$v = 15 \pm 3 \sqrt{2} i$ $v=15+-3sqrt2i$

Explanation:

$rearrange into standard form a x^{2} + b x + c = 0$ $"rearrange into standard form "ax^2+bx+c=0$

$\Rightarrow v^{2} - 30 v + 243 = 0$ $rArrv^2-30v+243=0$

$∙ coefficient of v^{2} term must be 1, which it is$ $• " coefficient of "v^2" term must be 1, which it is"$

$∙ add {(\frac{1}{2} coefficient of v-term)}^{2} to both sides$ $• " add "(1/2"coefficient of v-term")^2" to both sides"$

$\Rightarrow v^{2} + 2 (- 15) v + 225 + 243 = 0 + 225$ $rArrv^2+2(-15)vcolor(red)(+225)+243=0color(red)(+225)$

$\Rightarrow {(v - 15)}^{2} = 225 - 243 = - 18$ $rArr(v-15)^2=225-243=-18$

$there are no real solutions$ $"there are no real solutions"$

$take the square root of both sides$ $color(blue)"take the square root of both sides"$

$\Rightarrow v - 15 = \pm \sqrt{- 18} \leftarrow note plus or minus$ $rArrv-15=+-sqrt(-18)larr" note plus or minus"$

$\Rightarrow v - 15 = \pm 3 \sqrt{2} i$ $rArrv-15=+-3sqrt2i$

$\Rightarrow v = 15 \pm 3 \sqrt{2} i$ $rArrv=15+-3sqrt2i$

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How do you solve $v^{2} - 17 v + 200 = 13 v - 43$ $v^2-17v+200=13v-43$ by completing the square?

1 Answer

Explanation:

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How do you solve v^2-17v+200=13v-43v2−17v+200=13v−43v^2-17v+200=13v-43 by completing the square?

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Explanation:

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How do you solve $v^{2} - 17 v + 200 = 13 v - 43$ $v^2-17v+200=13v-43$ by completing the square?