Put simply, the equation for solving a cubic equation is x2 + 2ax +b = (x+a)2 + b-a2. This leads to x = -a +/- (a2 -b)1/2.
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What role of operations that applies when you are solving an equation does not apply when your solving an inequality?"
An equation is a mathematical statement that may (or may not) be true, defined for some variables. Solving an equation is finding those values of the variables for which the equation or statement is true.
An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).
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The roots of an equation in two variables is calculated by setting the dependent variable, y, equal to 0 and then solving the resulting equation for the independent variable, x. The procedure for solving the equation in x will depend on the nature of the equation.