SOLUTION: Find the smallest value of x such that x^2 + 10x + 25 = -x^2 + 5x + 32.

2x+7=0;     x-1=0
  2x=7;       x=1
   x=7/2
   x=3.5

Since 1 is smaller than 3.5, the answer is 1

Duh!

Edwin

              Step 1.  Reduce to the standard form quadratic equation


For it, collect all the terms in the left side and combine like terms.
You will get

    2x^2 + 5x - 7 = 0.



              Step 2.  Calculate the discriminant to determine if the roots are real


d = b^2 - 4ac = 5^2 - 4*2*(-7) = 25 + 56 = 81.


The discriminant is positive, so the roots are real numbers, 
and we can use the conception "greater-smaller" for them.



              Step 3.  Use the quadratic formula to find the smallest root


smallest root =  =  =  =  = -3 = -3.5.    ANSWER