SOLUTION: Please help me solve this problem by completing the square: {{{ 2h^2-5h+4=0 }}}.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help me solve this problem by completing the square: {{{ 2h^2-5h+4=0 }}}.      Log On


   

Question 269820: Please help me solve this problem by completing the square: +2h%5E2-5h%2B4=0+.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
step 1 - factor out 2 from the first and second term to get
2%28h%5E2+-+%285%2F2%29h+%2B+_____+%29=+-4+%2B+_____
the blanks are waiting for certain numbers.
step 2 - take (1/2) of the middl term and square it. Put that number in the first blank.
2%28h%5E2+-+%285%2F2%29h+%2B+%28-5%2F4%29%5E2%29+=+-4+%2B+_____
step 3 - squaring it gives us 25/16, but we multiply this by 2 since there are 2 groups of these. We get 50/16. Now put this number into the other blank space to get
2%28h%5E2+-+%285%2F2%29h+%2B+%28-5%2F4%29%5E2%29+=+-4+%2B+50%2F16
step 4 - rewrite the trinomial as a binomial squared and simplify the right side to get
2%28h-5%2F4%29%5E2+=+14%2F16
step 5 - divide by 2 and reduce to get
%28h-5%2F4%29%5E2+=+7%2F16
step 6 - take a square root to get
%28h-5%2F4%29+=+%2B-sqrt%287%29%2F4
step 7 - add 5/4 to get
h+=+%285%2B-sqrt%287%29%29%2F4