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Complete the squareTechnique

Technique

Complete the square

Add half the x-coefficient, squared, to both sides

3 min 3 steps

Every quadratic is one small piece away from a perfect square. Supplying missing pieces is new for me; I used to be the reason they went missing.

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Perfect squares, difference of squaresFactExpand squares in full and factor differences fast

Used by

Solve a nonlinear equationTacticLet the form pick the method, then check every root
Extract features of a quadratic functionTacticPick the form that shows the feature you need
Circle equations, points, and tangentsTacticGet to standard form, then read center and radius