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Solve a nonlinear equationTactic

Tactic

Solve a nonlinear equation

Let the form pick the method, then check every root

11 min 6 stepsGraded practice at the end

Nonlinear equations often hide a second solution, and sometimes a fake one. I once laminated a counterfeit library card, so fakes are a sore subject.

Meet it
Spot it
Run it
Dodge the traps
Play with it
Prove it

The first step is free. A free account opens the rest.

Calls on

Factor polynomialsTechniquePull out the common factor, then match a pattern
Complete the squareTechniqueAdd half the x-coefficient, squared, to both sides
Quadratic formula and discriminantTechniqueCollect to zero, read a, b, and c, then solve or count
Square both sides and checkTechniqueIsolate the radical, square, then test every solution
Absolute-value case splitTechniqueIsolate the bars, then solve the plus and minus cases
Clear fractions and decimalsTechniqueMultiply every term once and the fractions are gone
Isolate a variableTechniqueUndo each operation, in reverse, on both sides
Sum and product of rootsTechniqueGet the sum or product without finding the roots

Used by

Solve a nonlinear systemTacticSubstitute, keep every root, then find each y
Pythagorean theorem and trig ratiosTacticTurn one ratio and one side into the whole triangle
Circle equations, points, and tangentsTacticGet to standard form, then read center and radius

Other routes

Graph it (Desmos)TacticTurn the question into a point you can click
Backsolve from the choicesTacticTest the middle choice, then step up or down