By definition, you cannot. To solve means to find an answer or solution to a problem or a question. If there is no solution you cannot find one.
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Replace y = x2, and use the quadratic formula to solve for y. This should give you two solutions for y. Then replace back, and solve each of the solutions for y, to get two solutions each for x.
It depends entirely on the problem. There are specific solutions to specific problems.
Without an equality sign the given expression has no solutions
Yes.