Arrange, Then Root
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 44 of 63.
x^2 - 49 = 0 is a difference of squares, so you could factor it. There is a faster way. Move the 49 to the other side to get x^2 = 49, then take the square root of both sides: x = ±7.
Both methods give the same answers, 7 and -7. Factoring gives (x + 7)(x - 7) = 0, and then one factor must be zero. Taking square roots of x^2 = 49 gives x = ±7 in one step.
The first step is the same as in factoring: get the squared term alone on one side. Move the constant to the other side so that x^2 stands by itself, and only then take the square root.
Challenge
MediumSolve x^2 - 121 = 0 by taking square roots.
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: 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