A squared equation can have two solutions because a positive number and a negative number can have the same square. If the question asks for one possible value, you only need to find one branch. A Desmos regression with a restriction can do that; the trap is forgetting the negative branch.
Hints
- Hint 1
A square root of is a number whose square is . Both and work. What are the two possible values of the expression ?
- Hint 2
The negative branch has , so . A Desmos regression can find a solution on that branch if you restrict it to .
Step-by-step
Keep both signs, then find one solution
Step 1Recognize the two branches
Because , the squared expression could equal or : or . Don't discard the negative case. Squaring hides whether the expression started positive or negative.
- Step 2
Find a value on the negative branch
On the negative branch, , so . Type in Desmos. Replacing with and with makes this a regression; the braces keep its search below . Under PARAMETERS, Desmos shows . So is a possible value of . Choice D.