Question 931·Easy·Math

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\frac{(x-2)^2}{9}=16

What is the positive solution to the equation above?

A quadratic equation can have two solutions because a number and its negative have the same square. If the question asks for the positive solution, enter the equation as a Desmos regression and restrict the unknown to positive values. Apply the sign condition to the requested variable, not automatically to what sits inside the square.

Hints

Hint 1
A square has the same result for a number and its negative. So undoing the square on $(x-2)^2$ can give either sign for $x-2$ . Which quantity does the question say must be positive?
Hint 2
In a Desmos regression, use $x_1$ for the unknown and $\sim$ to make the two sides match. Add $\left\{x_1>0\right\}$ to keep only positive values of $x$ . The restriction belongs on $x$ , not $x-2$ .

Step-by-step

Restrict a Desmos regression to positive values
Step 1
Put the positive condition on the right quantity
A square hides whether the number inside it was positive or negative. So $(x-2)^2$ doesn't tell you the sign of $x-2$ . The question asks for positive $x$ , not positive $x-2$ ; keep that distinction when you solve.
Step 2
Solve with the positive restriction
Type $\frac{(x_1-2)^2}{9}\sim16\left\{x_1>0\right\}$ . In a Desmos regression, $x_1$ is the value to find, $\sim$ tells Desmos to match the two sides, and the braces require positive $x_1$ . Under PARAMETERS, Desmos shows $x_1=14$ , so the positive solution is $14$ . Choice C.

Question 931·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this