SOLUTION: {{{+x-7=7}}} x-7 is in square sign

Algebra ->  Rational-functions -> SOLUTION: {{{+x-7=7}}} x-7 is in square sign       Log On


   

Question 69673: %2Bx-7=7 x-7 is in square sign


Found 2 solutions by funmath, bucky:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
%2Bx-7=7 x-7 is in square sign
sqrt%28x-7%29=7
%28sqrt%28x-7%29%29%5E2=7%5E2
x-7=49
x-7%2B7=49%2B7
highlight%28x=56%29
With these type of equations, always check the solutions because you can do everything right and get an extraneous solution (false).
sqrt%2856-7%29=7
sqrt%2849%29=7
7=7 It works, x=56 is a valid solution.
Happy Calculating!!!

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
If I understand your problem correctly it is:
%28x-7%29%5E2+=+7
One of the ways to solve this is to take the square root of both sides to get:
x-7+=+%2B++sqrt%287%29 and x-7+=-sqrt%287%29
Then add + 7 to both sides and the result is:
x+=+7+%2B-+sqrt%287%29
If you calculate this you will find the two answers are about 9.645751311 and 4.354248689
Another way to solve it is to square out the left side of the equation by multiplying %28x-7%29%2A%28x-7%29. If you do that, the equation becomes:
x%5E2+-+14x+%2B+49+=+7
Subtract 7 from both sides to make the equation:
+x%5E2+-+14x+%2B+42+=+0
This is in the form for applying the quadratic formula that says if a quadractic equation is in the form:
ax%5E2+%2B+bx+%2B+c+=+0 then the solution for x is in the form:
x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29%29
For this problem a = 1, b = -14, and c = 42
Substituting the values of a, b, and c for this equation results in:
x+=+%28-%28-14%29+%2B-+sqrt%28%28-14%29%5E2-4%2A1%2A42%29%29%2F%282%2A1%29%29
If you work this out you will get the same answers as you got previously
Hope this helps.