Bud G. answered • 09/25/14
Tutor
New to Wyzant
HS/College Math Tutor-Certified HS with 13 years Exp
Two ways to answer this one!
Doing the Math. Use the standard form of ax^2 + bx + c. In this case a = 1, so it's a lot easier.
x^2 - 4x + 2 = 10
-2 -2 Subtract 2 from both sides
x^2 - 4x = 8 The left hand side is ready to complete; b = -4, so ...
The c term to complete the square is c = (b/2)^2 = (-4/2)^2 = (-2)^2 =4
x^2 - 4x +4 = 8 +4 Adding 4 to both sides completes the square on the left side.
(x - 2)^2 = 12 Your answer is A. Without multiple choice, you must know these steps to solve the problem.
But since it's multiple choice, you have an alternative if you panic and forget how to do the problem, skip it, work to the end, then return to this one and work each answer backwards. It's longer, but guess and check the answer.
Assume D. is what you think is the best answer. Now begin the check:
(x+2)^2 = 8
x^2 + 4x +4 = 8 Expand the square.
-2 -2 Subtract 2 from both sides so that the left hand side matches a and b in the original equation.
x^2 - 4x + 2 = 6 False. It should equal 10! Mark out this guess and go to the next best answer.
Notice this is also a technique to check your work when you do the math ...
(x+2)^2 = 12 Our answer when we did the math.
x^2 + 4x + 4 = 12
-2 -2 Subtract 2 from both sides so that the left hand side matches a and b in the original equation.
x^2 - 4x + 2 = 10 True; we've matched the original equation. We've verified our first answer A as correct.
Now you're a pro at how to work these types of problems based upon the testing method!
Extra special bonus: If a does not = 1, then c = (b/[2a])^2.
