Question 1039·Easy·Math

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Which of the following numbers is a solution to the equation $(x-3)^{2}=25$ ?

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 $25$ is $5$ , but both $5^2$ and $(-5)^2$ equal $25$ . What two values could the entire expression inside the parentheses have?
Hint 2
Add $3$ 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 1
Undo the square in two ways
A square is $25$ when its base is $5$ or $-5$ , so the expression being squared has two possible values: $x-3=5\quad\text{or}\quad x-3=-5$ . Keep both signs when undoing a square.
Step 2
Check the positive case
For the positive case $x-3=5$ , add $3$ to both sides: $x=8$ . That isn't among the choices, so any listed solution must come from the other case.
Step 3
Find the listed solution
Type $(x_1-3)^2\sim25\{x_1<0\}$ in Desmos. Replacing $x$ with $x_1$ and $=$ with $\sim$ makes this a regression: Desmos finds a value that makes the sides match. The restriction keeps the negative solution. Under PARAMETERS, Desmos shows $x_1=-2$ , so $-2$ solves the equation. Choice D.

Question 1039·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this