Split the Plus-Minus
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 50 of 63.
After the root is worked, one line holds both answers: x = (-5 ± 1) / 2. The ± is a textbook's way of carrying two equations in one, and the finishing move is to split it: the plus case x = (-5 + 1) / 2 = -2, the minus case x = (-5 - 1) / 2 = -3.
On the board the split is your move, exactly like the zero product split: tap the line and break it into its two cases, then work each one's arithmetic to a plain number.
Keep the two cases apart to the end. Adding first and subtracting later inside one line is where signs get tangled; two short case lines stay honest, and each lands on one of the two answers.
Challenge
MediumSolve x^2 + 9x + 8 = 0 with the quadratic formula, splitting the plus-minus.
Try it yourself
Solve for x
This 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: Signs7The Zero Product Rule
A Product That Makes ZeroOne Factor Is EnoughThe Bare XEvery Factor Gets a TurnRecap: Zero Product10The Quadratic Formula
The Formula, StatedThe Number Under the RootSplit the Plus-MinusIt Always WorksChoosing a MethodRecap: The Formula2The 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 Completely