SOLUTION: complete the square x^2-14x=51 x= ? and ?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: complete the square x^2-14x=51 x= ? and ?      Log On


   

Question 87887: complete the square
x^2-14x=51
x= ? and ?
Found 2 solutions by rapaljer, stanbon:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-14x=51+

Assuming that the coefficient of x%5E2 is 1, you must take HALF of the x coefficient and SQUARE it, adding this quantity to each side of the equation as follows:
x%5E2+-14x+%2B_____=+51+%2B+____ Half of -14 is -7, and (-7)^2= 49!
x%5E2+-14x%2B49=+51+%2B+49
%28x-7%29%5E2+=+100

Take the square root of each side:
+%28x-7%29+=+0%2B-+sqrt%28100%29+

Add +7 to each side:
x=+7%2B-+10+
x=+7%2B10=17 x=7-10=-3

By the way, since this came out to a square root of a perfect square, like 100, it means that the problem could have been solved by factoring!!

R^2 Retired from SCC


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
complete the square
x^2-14x=51
x^2-14x+(14/2)^2 = 51+(14/2)^2
(x-7)^2 = 51 + 49
x-7 = +-10
x= 10+7= 17 or x= -10+7=-3
====================
Cheers,
Stan H.