SOLUTION: {{{x^2-4x+2=0}}} Please show me the working out to get {2 - sprt(2), 2 + sqrt(2)}

Algebra ->  Equations -> SOLUTION: {{{x^2-4x+2=0}}} Please show me the working out to get {2 - sprt(2), 2 + sqrt(2)}      Log On


   

Question 516139: x%5E2-4x%2B2=0
Please show me the working out to get {2 - sprt(2), 2 + sqrt(2)}
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+-+4x+%2B+2+=+0+
+x%5E2+-+4x+=+-2+
You can complete the square.
Take 1/2 of the coefficient of x,
square it , and add it to both sides
+x%5E2+-+4x+%2B+%28-4%2F2%29%5E2+=+-2+%2B+%28-4%2F2%29%5E2+
+x%5E2+-+4x+%2B+4+=+-2+%2B+4+
+%28+x+-+2%29%5E2+=+2+
Take the square root of both sides
+x+-+2+=+sqrt%282%29+
and also
+x+-+2+=+-sqrt%282%29+
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So, the roots are:
+x+=+2+%2B+sqrt%282%29+
+x+=+2+-+sqrt%282%29+