How do I solve this equation? #y^2+35=8y#
Do I divide the #35# by #y# as well as the #y^2# and the #8y# ? Or maybe I solve it as a quadratic?
Do I divide the
3 Answers
See below.
Explanation:
Mind that
now comparing with
we have
At this point we have a real impossibility so the equation has no solution for real values.
Trying the complex domain we can state
In the complex domain, the solution arise from
You do not solve this equation by division. This is a quadratic equation ; there are several ways to solve it. I will explain a solution below.
Explanation:
Given:
Subtract
This is in a special case of the standard form
where
There is something called a discriminant that will tell you whether this equation has, 0, 1, or 2 solutions.
The discriminant is:
Substituting in our special values:
Because the discriminant is negative, we know that the equation has no real solutions; its solutions are a complex conjugate pair. I suspect that you have not, yet, learned about the complex number system so we must declare that this quadratic has no solutions.
This equation has no solution.
Explanation:
As soon as you have
There are now 3 options:
As this does not factorise, I will choose to complete the square.
And here we have a problem, because
This equation has no solution.
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Remember that you may not divide by a variable unless you are sure it is not equal to