A Squared Package
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 45 of 63.
The squared thing need not be a bare x. (x + 3)^2 = 16: the PACKAGE x + 3 is squared, so un-square the package: x + 3 = ±4.
Two little equations remain: x + 3 = 4 gives x = 1, and x + 3 = -4 gives x = -7. The root move does the splitting; Fundamentals moves finish each case.
This shape is why the perfect squares of chapter five matter: any equation that can be WRITTEN as a squared package equals a number surrenders to two square roots and a subtraction. Keep the package whole while you root; open it after.
Challenge
MediumSolve (x - 2)^2 = 25. Root the package, then open it.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factoring & Quadratics
1What Factoring Is
Two DirectionsThe Reverse GearUn-Distributing LettersThe Check Is MultiplicationRecap: First Factors4Minus Signs in the Machine
A Negative ProductWhich One Gets the MinusBoth NegativeThe Sign MapRecap: Signs2The Greatest Common Factor
Number and Letter TogetherThe Largest OneHigher PowersThree Terms Share TooRecap: The GCF5Special Shapes
A Missing MiddleThe Shape in LettersThe Perfect SquareThe Minus VersionPrime PolynomialsRecap: Special Shapes3The Sum-Product Machine
Reading the ProductHunting the PairThe Machine in LettersLonger HuntsRecap: The Machine6Factor Completely
Two LayersSquares InsideCompletely Means CompletelyThe Deep CheckRecap: Factor Completely9The Square Root Method
Undoing a SquareArrange, Then RootA Squared PackageRoots That Are Not WholeRecap: Square Roots