How do you solve the equation #3x^2-x+5=x^2+3x-14# by completing the square?

1 Answer
marfre
Feb 15, 2017

#2(x-1)^2+17 = 0#

Explanation:

Combine like terms by moving all terms on the right to the left:
#(3x^2-x^2) +(-x-3x) +(5+14) = 0#

Simplify: #2x^2 -4x +19 = 0#

Complete the square:

  1. Combine the x-terms & factoring: #2(x^2-2x) +19 = 0#
  2. Half the x-term #-2x: 1/2(-2) = -1#, Used in #(x-1)^2#
  3. Square the halved x-term from step 2: #(-1)^2 = 1#, and multiply by #2#, the factored number in front of the square.
  4. Complete the square & subtract the added term: #2(x-1)^2 +19 - 2(1) = 0#
  5. Simplify: #2(x-1)^2 +17 = 0#
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