Question 269820
step 1 - factor out 2 from the first and second term to get
{{{2(h^2 - (5/2)h + _____ )= -4 + _____}}}
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(h^2 - (5/2)h + (-5/4)^2) = -4 + _____}}}
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(h^2 - (5/2)h + (-5/4)^2) = -4 + 50/16}}}
step 4 - rewrite the trinomial as a binomial squared and simplify the right side to get
{{{2(h-5/4)^2 = 14/16}}}
step 5 - divide by 2 and reduce to get
{{{(h-5/4)^2 = 7/16}}}
step 6 - take a square root to get
{{{(h-5/4) = +-sqrt(7)/4}}}
step 7 - add 5/4 to get
{{{h = (5+-sqrt(7))/4}}}