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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 99 E (page 885)

In the following exercises, solve by completing the square.
$3 m^{2} + 30 m - 27 = 6$

Short Answer

Expert verified

The solution is $m = - 11, m = 1$ .

Step by step solution

01

Step 1. Given information

Equation: $3 m^{2} + 30 m - 27 = 6$

02

Step 2. Calculation

We have,

$3 m^{2} + 30 m - 27 = 6$

$3 (m^{2} + 10 m - 9) = 3 (2)$

localid="1645163752120" $\frac{3 (m^{2} + 10 m - 9)}{3} = \frac{3 (2)}{3}$

localid="1645163853795" $m^{2} + 10 m - 9 = 2$

$m^{2} + 10 m - 9 + 9 = 2 + 9$

$m^{2} + 10 m = 11$

localid="1645163922467" $m^{2} + 10 m + {(\frac{1}{2} 路 (10))}^{2} = 11 + {(\frac{1}{2} 路 (10))}^{2}$

localid="1645163946899" $m^{2} + 10 m + {(5)}^{2} = 11 + {(5)}^{2}$

localid="1645163964764" $m^{2} + 10 m + 25 = 11 + 25$

localid="1645164005576" ${(m + 5)}^{2} = 36$

$\sqrt{{(m + 5)}^{2}} = \sqrt{36}$

localid="1645164332028" $m + 5 = 卤 6$

$m + 5 = - 6, m + 5 = 6$

localid="1645164378725" $m + 5 - 5 = - 6 - 5, m + 5 - 5 = 6 - 5$

localid="1645164386296" $m = - 11, m = 1$

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