SOLUTION: can you explain this to me please solve by completing the squaqr root property. x^2 + 8x + 13 = 0 thank you julie

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Question 118185: can you explain this to me please
solve by completing the squaqr root property.
x^2 + 8x + 13 = 0
thank you
julie
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve by completing the squaqr root property.
x^2 + 8x + 13 = 0
:
x^2 + 8x + ___ = -13; subtracted 13 from both sides
:
To complete the square, square half the coefficient of x, 4^2 = 16
x^2 + 8x + 16 = -13 + 16; added 16 to both sides
:
(x + 4)^2 = +3;
:
x + 4 = +/-sqrt%283%29; find the square root of both sides
:
x = -4 + sqrt%283%29; subtract 4 from both sides
and
x = -4 - sqrt%283%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B8x%2B13=0 Start with the given equation


x%5E2%2B8x=-13 Subtract 13 from both sides


Take half of the x coefficient 8 to get 4 (ie 8%2F2=4)
Now square 4 to get 16 (ie %284%29%5E2=16)



x%5E2%2B8x%2B16=-13%2B16 Add this result (16) to both sides. Now the expression x%5E2%2B8x%2B16 is a perfect square trinomial.




%28x%2B4%29%5E2=-13%2B16 Factor x%5E2%2B8x%2B16 into %28x%2B4%29%5E2 (note: if you need help with factoring, check out this solver)



%28x%2B4%29%5E2=3 Combine like terms on the right side

x%2B4=0%2B-sqrt%283%29 Take the square root of both sides

x=-4%2B-sqrt%283%29 Subtract 4 from both sides to isolate x.

So the expression breaks down to
x=-4%2Bsqrt%283%29 or x=-4-sqrt%283%29


So our answer is approximately
x=-2.26794919243112 or x=-5.73205080756888

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B8x%2B13%29+ graph of y=x%5E2%2B8x%2B13


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=-2.26794919243112 and x=-5.73205080756888, so this verifies our answer.