Treat the left-hand side and right-hand side of the equation as separate functions. We are going to have to use a graphing calculator for this.
x≈ - 3.17
Practice makes perfect
This equation cannot be solved algebraically. To solve it, we have to use a graphing calculator. We should treat the left-hand side and right-hand side as separate functions.
3^x+5= x^2-5
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f(x)= 3^x+5 and g(x)= x^2-5
To draw these graphs on the calculator, push the Y= button and type the functions on two of the rows. Having written the function, we can push GRAPH to draw them.
As we can see, the two functions intersect at around x≈ - 3. Note that the functions will not intersect after this first intersection, as 3^x+5 grows much faster than x^2-5. To find the point of intersection, push 2nd and CALC and choose the fifth option, intersect. Choose the first and second curve and pick a best guess for the point of intersection.
