SOLUTION: solve for a by completing the square: a^2-10a+1=0

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Question 45332: solve for a by completing the square:
a^2-10a+1=0
Found 2 solutions by Nate, tutorcecilia:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
a^2 - 10a + 1 = 0
a^2 - 10a = -1
(a - 5)^2 = 24
a - 5 = +- 2sqrt(6)
a = 5 +- 2sqrt(6)

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
a^2-10a+1-1=0-1 [Subtract 1 from both sides]
a^2-10a = -1 [Simplify]
a^2-10a + (10/2)^2 = -1 [Divide and square the second coefficient]
a^2-10a + (10/2)^2 = -1 + (10/2)^2 [Add it to both sides of the equation]
a^2-10a + (5)^2 = -1 + (5)^2 [Simplify]
a^2-10a + (5)^2 = -1 + 25 [Further simplify the right hand side only]
a^2-10a + (5)^2 = 24 [Further simplify the right hand side of the equation only]
(a-5)(a-5) = 24 [Factor the polynomial]
%28%28sqrt%28a-5%29%29%5E2%29={{sqrt(24)}}} [Take the square root of both sides]
a-5 = +-2sqrt%286%29 [Simplify]
a-5+5 = +-2sqrt%286%29 +5 [Solve for "a"]
a = +-2sqrt%286%29 +5
a = 5+-2sqrt%286%29 [The two answers]
a = 5 + 2sqrt%286%29 or 5 - 2sqrt%286%29