math: help me solve for [H+] given eqtn [H+]²+Ka[H+]-Kax=0?
solve for [H+] given eqtn [H+]²+Ka[H+]-Kax=0
Ka is given as 1.75*10^-5 by the way. so ka is a constant and [H+] and x is a variable.
i think i'm supposed to use the quadratic eqtn. but i can't get the right answer (or the answer the book got)
[H+] = (1/2)* (-Ka + sqrt[Ka² + 4Kax])
Thanks!
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Use the quadratic equation, or complete the square. Using quadratic equation:
a = 1
b = Ka
c = -Kax...in a quadratic equation, the entire last term is a constant. "x" is part of the constant.
-b +/- √b^2 - 4 ac. All over 2, which is the same as multiplying by 1/2
(1/2)(-Ka +/- √[(Ka^2) - (4)(1)(-Kax)]
(1/2)(-Ka +/- √[(Ka^2) + 4Kax]
They seem to be using only the principal (positive) root?