Solve the equation by graphing.
5 = -√x-3
I don't know how to make the graph. What would the graph look like? I worked out the equation and this is what it came out to be: 5 ≠ -5, which is no solution. Is there a way to graph this? Sorry, confused... please help.
Since the domain of √x is x>=0, you will need (x-3) >= 0. That is, x >= 3.
So, plug in some values of x and plot the points for y=-√(x-3):
x y
3 0
4 -1
7 -2
12 -3
...
It will look like the bottom half of a horizontal parabola with vertex at (3,0). The equation could also be written as
y^2 = x-3
x = y^2+3
However, your "no solution" answer is correct. √(x-3) is always positive, so -√(x-3) can never be 5.
To graph the equation and find the solutions, let's start by rearranging the equation to isolate the square root term:
-√(x - 3) = 5
To remove the negative sign, we can square both sides of the equation:
(-√(x - 3))^2 = (5)^2
(x - 3) = 25
Now, let's solve for x:
x = 25 + 3
x = 28
So, the equation simplifies to x = 28.
To graph this equation, we can plot the points on a coordinate plane. Since x = 28 is a single value, it corresponds to a single point on the graph, which is (28, 0). So, the graph would consist of a single point on the x-axis at x = 28.
Based on your calculations that 5 ≠ -5, it seems there may have been an error in your working. It's crucial to be meticulous with calculations to ensure the accuracy of the solution.