How do you solve $c^{2} + 8 c + 2 = 5 c + 15$ $c^2 + 8c + 2 = 5c + 15$ by completing the square?

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How do you solve $c^{2} + 8 c + 2 = 5 c + 15$ $c^2 + 8c + 2 = 5c + 15$ by completing the square?

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Answer 1 · 2018-04-25T07:45:02

See the Explanation:

Explanation:

$c^{2} + 8 c + 2 = 5 c + 15$ $c^2 + 8c + 2 = 5c + 15$
$c^{2} + 3 c = 13$ $c^2 + 3c = 13$
$c^{2} + 2 (\frac{3}{2}) c = 13$ $c^2 + 2(3/2)c = 13$
$c^{2} + 2 (\frac{3}{2}) c + {(\frac{3}{2})}^{2} - {(\frac{3}{2})}^{2} = 13$ $c^2 + 2(3/2)c + (3/2)^2 - (3/2)^2 = 13$
${(c + \frac{3}{2})}^{2} - {(\frac{3}{2})}^{2} = 13$ $(c + 3/2)^2 - (3/2)^2 = 13$
${(c + \frac{3}{2})}^{2} = 13 + \frac{9}{4}$ $(c + 3/2)^2 = 13 + 9/4$
$c + \frac{3}{2} = \pm \sqrt{13 + \frac{9}{4}}$ $c + 3/2 = +- sqrt(13 + 9/4)$
$c = - \frac{3}{2} \pm \frac{\sqrt{61}}{2}$ $c = -3/2 +- sqrt61/2$

Answer 2 · 2018-04-25T07:54:46

$c = - \frac{3}{2} \pm \frac{1}{2} \sqrt{61}$ $c=-3/2+-1/2sqrt61$

Explanation:

$rearrange equation into standard form$ $"rearrange equation into "color(blue)"standard form"$

$subtract 5 c + 15 from both sides$ $"subtract "5c+15" from both sides"$

$\Rightarrow c^{2} + 3 c - 13 = 0 \leftarrow in standard form$ $rArrc^2+3c-13=0larrcolor(blue)"in standard form"$

$using the method of completing the square$ $"using the method of "color(blue)"completing the square"$

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

$∙ add/subtract {(\frac{1}{2} coefficient of the c-term)}^{2} to$ $• " add/subtract "(1/2"coefficient of the c-term")^2" to"$
$c^{2} + 3 c$ $c^2+3c$

$c^{2} + 2 (\frac{3}{2}) c + \frac{9}{4} - \frac{9}{4} - 13 = 0$ $c^2+2(3/2)c color(red)(+9/4)color(red)(-9/4)-13=0$

$\Rightarrow {(c + \frac{3}{2})}^{2} - \frac{61}{4} = 0$ $rArr(c+3/2)^2-61/4=0$

$\Rightarrow {(c + \frac{3}{2})}^{2} = \frac{61}{4}$ $rArr(c+3/2)^2=61/4$

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

$\Rightarrow c + \frac{3}{2} = \pm \sqrt{\frac{61}{4}} \leftarrow note plus or minus$ $rArrc+3/2=+-sqrt(61/4)larrcolor(blue)"note plus or minus"$

$\Rightarrow c + \frac{3}{2} = \pm \frac{1}{2} \sqrt{61}$ $rArrc+3/2=+-1/2sqrt61$

$subtract \frac{3}{2} from both sides$ $"subtract "3/2" from both sides"$

$\Rightarrow c = - \frac{3}{2} \pm \frac{1}{2} \sqrt{61} \leftarrow exact solutions$ $rArrc=-3/2+-1/2sqrt61larrcolor(red)"exact solutions"$

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How do you solve $c^{2} + 8 c + 2 = 5 c + 15$ $c^2 + 8c + 2 = 5c + 15$ by completing the square?

2 Answers

Explanation:

Explanation:

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How do you solve c2+8c+2=5c+15c^2 + 8c + 2 = 5c + 15 by completing the square?

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Explanation:

Explanation:

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How do you solve $c^{2} + 8 c + 2 = 5 c + 15$ $c^2 + 8c + 2 = 5c + 15$ by completing the square?