Question

name:
tbt#1 due thurs.
directions: show all your work to receive full credit.

1. solve by completing the square.

$x^2 + 12x + 43 = 0$
(handwritten steps: $x^2 + 12x = -43$; $x^2 + 12x + 36 = -43 + 36$; $sqrt{(x + 6)^2} = sqrt{-7}$; $x + 6 = pm...$)

Explanation:

Step1: Isolate constant term

$x^2 + 12x = -43$

Step2: Complete the square

Take half of 12, square it ($6^2=36$), add to both sides:
$x^2 + 12x + 36 = -43 + 36$
$(x+6)^2 = -7$

Step3: Solve for x using imaginary numbers

Take square root of both sides, use $i=\sqrt{-1}$:
$x+6 = \pm\sqrt{-7} = \pm i\sqrt{7}$

Step4: Isolate x

$x = -6 \pm i\sqrt{7}$

Answer:

$x = -6 + i\sqrt{7}$ and $x = -6 - i\sqrt{7}$