Question 157·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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The equation is

(x+1)^2 = 64

What is the positive value of x that satisfies the equation?

Your answer

A squared expression equal to a number signals a square-root equation: the expression inside the square can have a positive or negative value. If the question asks for the positive solution, you can restrict a Desmos regression to positive inputs. Don’t mistake the square root for $x$ when the expression being squared contains more than $x$ .

Hints

Hint 1
The number $64$ is a square, and two numbers have that square: one positive and one negative. What two values could the whole expression $x+1$ have?
Hint 2
A regression lets Desmos find a value that makes an equation true. To get the positive solution, replace $x$ with $x_1$ , replace $=$ with $\sim$ , and restrict $x_1>0$ .

Step-by-step

Keep both signs, then find the positive solution
Step 1
Undo the square with both signs
A square root undoes a square. Since both $8^2$ and $(-8)^2$ equal $64$ , keep both signs for the whole expression inside the square: $x+1=\pm 8$ . The $8$ is a value of $x+1$ , not necessarily $x$ .
Step 2
Find the positive value of x
Type $(x_1+1)^2\sim64\left\{x_1>0\right\}$ in Desmos. The $x_1$ tells Desmos to solve for a value instead of graphing $x$ ; $\sim$ asks it to match the two sides. The restriction keeps only positive values. Under PARAMETERS, Desmos shows $x_1=7$ . So the positive value of $x$ that satisfies the equation is $7$ . Grid in 7.

Question 157·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this