When real numbers fail to provide a solution there is no real solution - its as simple as that!
There is no integer solution for 2x = 3. To find a solution you need to extend the domain to rational numbers. There is no rational number solution to x^2 = 2, so you need to extend to the real numbers.
For some equations that do not have a real solution, for example, x^2 + 1 = 0, there are solutions if the domain is extended to the complex field.
x + 2 = x - 2 has no real solution nor a complex solution. However, it does have a solution in modulo 4 arithmetic. But in that case the original equation should have said so. When seeking a solution to an equation, it is customary to define the domain in which the answer (if any) may be found. - unless the context makes the domain clear.
0
The result is all real numbers.
Here are a few: 0 = 1 x = x + 1 (subtract "x" on each side, and you get the previous one!) x2 = -1 (if you want real numbers; however, it has two solutions in the complex numbers) ln x = -1 (same as above: no solution in the real numbers, but it has a solution in the complex numbers) ln x = 0 (no solution, neither in the real numbers, nor in the complex numbers) 0x = 5
no solution
The complex roots of an equation is any solution to that equation which cannot be expressed in terms of real numbers. For example, the equation 0 = x² + 5 does not have any solution in real numbers. But in complex numbers, it has solutions.
It depends on the domain.
The answer to the question depends on the set of numbers within which you are working. If you are working in integers, x2 = 2.25 has no solution. However, it does have a solution in rational numbers (x = 1.5). If working with rationals, x2 = 6 has no rational solution but it does have a solution in real numbers. Yet again, x2 = -6 has no solution in the reals, but does have a solution in complex numbers.
That is how an identity is defined. If the solution was not true for all numbers, then it would not be called an identity. In fact, it should be true for all complex numbers as well.
A solution with all real numbers indicates that the equation or inequality has no restrictions on its values, meaning any real number can satisfy it. Graphically, this is often represented as a horizontal line on a number line or as a shaded region extending infinitely in both directions. For example, the equation (x = x) or the inequality (x > -\infty) includes every possible real number as a solution. Essentially, it signifies that the solution set is the entire continuum of real numbers.
It is an equation which is insoluble in its domain. However, it may be soluble in a bigger domain.For example, x2 = 2 has no solution in the domain of rational numbers but it does in the real numbers, orx2 = -2 has no solution in the domain of real number but it does in imaginary numbers.
All real numbers.
WikiAnswers does not provide phone numbers.