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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.418. (page 982)

Solve by completing the square.
$t^{2} - 12 t = - 40$

Short Answer

Expert verified

The solution is $t = 卤 2 i + 6$ .

Step by step solution

01

Step 1. Given information.

The given equation is $t^{2} - 12 t = - 40$ .

02

Step 2. Simplify the equation.

$\begin{array}{rcl} t^{2} - 12 t & = & - 40 \\ t^{2} - 2 路 t 路 6 & = & - 40 \\ t^{2} - 2 路 t 路 6 + 36 & = & - 40 + 36 鈰� 鈰� (a d d 36 o n b o t h s i d e s) \\ t^{2} - 2 路 t 路 6 + 6^{2} & = & - 4 \\ {(t - 6)}^{2} & = & - 4 \\ t - 6 & = & 卤 \sqrt{- 4} \\ t - 6 & = & 卤 \sqrt{4} 路 \sqrt{- 1} \\ t - 6 & = & 卤 2 i 鈰� 鈰� (i = \sqrt{- 1}) \\ t - 6 & = & 卤 2 i \\ t & = & 卤 2 i + 6 \end{array}$

03

Step 3. Simplified answer.

Hence, the required solution is $t = 卤 2 i + 6$ .

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