anonymous
  • anonymous
how do i find the zeros of this quadratic equation by completing the square? x2+10x+29
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
to understand how to complete a square, you must first realize what a complete square looks like a complete square is of the form (x+n)^2; can you expand that out for me?
anonymous
  • anonymous
no i cant i dont think.whats the first step i could take in this problem?
amistre64
  • amistre64
(x+n)^2 is jsut (x+n) (x+n) they go over some memory technique called "foil" if that rings a bell

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anonymous
  • anonymous
yes i know how to do foil
amistre64
  • amistre64
then can you foil (x+n)(x+n) for me
anonymous
  • anonymous
Xsquared+xn+nx+Nsquared
amistre64
  • amistre64
good, lets clean that up into: x^2 + 2n x + n^2 this is what a complete square looks like lets compare that to what they gave you. x^2 + 10 x + 29 notice that we would love to have an n^2 in this someplace so lets find n 2n = 10, solve for n
anonymous
  • anonymous
n=5
amistre64
  • amistre64
great, then a complete square would look like: x^2 + 10 x + 25 would you agree that we have: x^2 + 10 x + 25 + 4 ??
anonymous
  • anonymous
where did the 4 come from?
amistre64
  • amistre64
well, we are given x^2 + 10 x + 29, notice that 25+4 = 29 ------------------------------------------- since (x+n)^2 = x^2 + 2n x + n^2, we can compress the expanded parts back into its little package again x^2 + 10 x + 25 + 4 (x^2 + 10 x + 25) + 4 (x+5)^2 + 4 and of course the zeroes or roots are when this equals zero (x+5)^2 + 4 = 0 ; can you think of a way to solve for x?
amistre64
  • amistre64
we could have also just said: since 25-25 = 0, just add this zero to it x^2 + 10 x + 29 x^2 + 10 x + 29 + 25 - 25 x^2 + 10 x + 25 + 29 - 25 x^2 + 10 x + 25 + 4
anonymous
  • anonymous
factor?
amistre64
  • amistre64
we cant really factor at the moment, but was have made life easier by compressing the complete square back into its package
amistre64
  • amistre64
(x+5)^2 + 4 = 0 ; -4 (x+5)^2 = -4 ; take the sqrt of each side to undo that ^2 x+5 = \(\pm \sqrt{-4}\) ; and finish off by -5 x = -5 \(\pm \sqrt{-4}\)
anonymous
  • anonymous
okay i see why you undid the ^2 so would that be my final answer?
amistre64
  • amistre64
it might need to be made more proper, something about an "i" ; but yes, thats the bulk of it
anonymous
  • anonymous
thanks i actually understand that haha
amistre64
  • amistre64
:) good luck
anonymous
  • anonymous
thank you:)
mathstudent55
  • mathstudent55
This is a great explanation of how completing the square works. Thanks, @amistre64
anonymous
  • anonymous
\[x ^{2}+10x=0-29\] \[adding both sides \left( \frac{ co-efficient of x }{2 } \right)^{2}i.e.,\left( \frac{ 10 }{ 2 } \right)^{2} or 25 ,we get\] \[x ^{2}+10x+25=-29+25=-4=4\iota ^{2}\] \[\left( x+5 \right)^{2}=\left( 2\iota \right)^{2}\] \[x+5=\pm2\iota \] solve and get the solution.

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