A squared expression can equal a positive number in two ways: the expression inside can be positive or negative. Keep both signs, then solve for the variable rather than stopping at the square root. If the choices make a sign restriction useful, a Desmos regression can find the solution with that sign.
Hints
- Hint 1
The square root of is , but both and equal . What two values could the entire expression inside the parentheses have?
- Hint 2
Add to solve the positive case, then compare its result with the choices. If no choice matches, a restriction in Desmos can help you find the other solution.
Step-by-step
Keep both signs, then use Desmos
Step 1Undo the square in two ways
A square is when its base is or , so the expression being squared has two possible values: . Keep both signs when undoing a square.
- Step 2
Check the positive case
For the positive case , add to both sides: . That isn't among the choices, so any listed solution must come from the other case.
- Step 3
Find the listed solution
Type in Desmos. Replacing with and with makes this a regression: Desmos finds a value that makes the sides match. The restriction keeps the negative solution. Under PARAMETERS, Desmos shows , so solves the equation. Choice D.