SOLUTION: I have plugged this one into the solver and that confused me even more. Solve by completing the square: x^2 + 8x + 13 = 0 I get to (x+4)^2 =3 and then I hit a wall. Please

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I have plugged this one into the solver and that confused me even more. Solve by completing the square: x^2 + 8x + 13 = 0 I get to (x+4)^2 =3 and then I hit a wall. Please      Log On


   

Question 118925: I have plugged this one into the solver and that confused me even more.
Solve by completing the square:
x^2 + 8x + 13 = 0
I get to (x+4)^2 =3 and then I hit a wall.
Please help!!
You guys are great and thank you in adavnce for your help.
Found 2 solutions by tutor_paul, HyperBrain:
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B8x%2B13=0
First, get all the x terms on one side of the equation:
x%5E2%2B8x=-13
Divide the coefficient of x by 2 and square the result. Add this result to both sides of the equation:
x%5E2%2B8x%2B16=-13%2B16
Simplify right side of the equation:
x%5E2%2B8x%2B16=3
Express the right side as a perfect square:
%28x%2B4%29%5E2=3
Remember the goal is to solve for x. Take the square root of both sides of the equation:
(x+4)=+-sqrt(3)
Since this is a second order equation, x can assume 2 values. Take the case of the %2Bsqrt%283%29 first and solve for x:
x%2B4=sqrt%283%29
highlight%28x=sqrt%283%29-4%29
Now, take the case of -sqrt%283%29:
x%2B4=-sqrt%283%29
highlight%28x=-sqrt%283%29-4%29
Plug each of these results into the original equation to check and see if they are right.
==================
good Luck,
tutor_paul@yahoo.com

Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Remember;
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2

GIVEN:
x%5E2%2B8x%2B13

Here, a%5E2=x%5E2 so a=x
Also, here, 2ab=8x so ab=4x
We have ab=4x and a=x
Solving simultaneously,
%28x%29b=4x
bx=4x
b=4

Now we know a=x and b=4

Finding %28a%2Bb%29%5E2,
%28a%2Bb%29%5E2=%28x%2B4%29%5E2=x%5E2%2B2%284x%29%2B16=x%5E2%2B8x%2B16

To be x%5E2%2B8x%2B16, we just add 3 to x%5E2%2B8x%2B13,

x%5E2%2B8x%2B13=0
x%5E2%2B8x%2B13%2B3=0%2B3
x%5E2%2B8x%2B16=3
%28x%2B4%29%5E2=3
sqrt%28%28x%2B4%29%5E2%29=sqrt%283%29
x%2B4=0%2B-sqrt%283%29
x=4%2B-sqrt%283%29

Power up,
HyperBrain!