How many are you expecting ? How will you know if we give you all of them,
or only some of them ?
Since the highest power of the variable in the equation is '2', ("x2"),
the equation has exactly two solutions.
25x2 - 100 = 0
Divide each side by 25:
x2 - 4 = 0
Add 4 to each side:
x2 = 4
Take the square root of each side:
x = +4 and -4
And there are your two solutions.
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No. Some have two solutions where as some have none.
the Bratu's equation is a differential equation which is non-linear (such as, if we have some solutions for it, a linear combinaison of these solutions will not be everytime a solution). It's given by the equation y''+a*e^y=0 or d²y/dy² =-ae^y.
7
The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.
A solution to an linear equation cx + d = f is in the form x = a for some a, we call a the solution (a might not be unique). Rewrite your sentence: x = 8, 8 is unique. So how many solution does it have?