Graph each side of the equation in a graphing calculator. Then, use the intersect feature.
x=7, see solution.
Practice makes perfect
Consider the given equation.
sqrt(x+1)=sqrt(x-3)
Let's solve this equation by using our graphing calculator! We need to write each side of the equation as a function. We begin by pressing the Y= button and writing each side of the equation in two different rows.
Since the right hand of the equation is a square root, the radicand cannot be negative. We will change the window settings to include this.
Now we push the GRAPH button.
In order to find the point of intersection, we will begin by pressing 2nd, CALC, and choosing the fifth option, intersect.
Choose the first and second curve, and pick a best guess for the point of intersection.
We found that the point of intersection is ( 7,2). Therefore, x= 7 is the solution to the equation.
Alternative Solution
Using a Table of Values
We can also use a table of values to solve this equation. Since the right side of the equation is a square root, the radicand cannot be negative. We will start from x=3.
x
sqrt(x+1)
Simplify
sqrt(x-3)
Simplify
3
sqrt(3+1)
≈ 1.59
sqrt(3-3)
0
4
sqrt(4+1)
≈ 1.71
sqrt(4-3)
1
5
sqrt(5+1)
≈ 1.82
sqrt(5-3)
≈ 1.41
6
sqrt(6+1)
≈ 1.91
sqrt(6-3)
≈ 1.73
7
sqrt(7+1)
2
sqrt(7-3)
2
We found that when x=7, both sides of the equation are equal to 2. Therefore x=7 is a solution to the given equation.
