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Solve for x in the following equation.
Answer: The exact answer is and the approximate answer is
In order to solve this equation, we have to isolate the exponential term. Since we cannot easily do this in the equation's present form, let's tinker with the equation until we have it in a form we can solve.
The left side of the equation is not easily factored. Let's see if we can use the Quadratic Formula.
Note that the equation can be rewritten as This is a quadratic equation in If it is easier for you, substitute a number, say p, in place of and rewrite the equation as let's solve this equation for p.
However, the initial equation did not contain p, therefore you have to resubstitute for p and solve for x.
There is no real number such that a negative number.
The exact answer is and the approximate answer is These answers may or may not be solutions to the original equations. You must check the answers in the original equation.
Check this answer in the original equation.
Check the solution by substituting 0.762831450377 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.
You can also check your answer by graphing (formed by subtracting the right side of the original equation from the left side). Look to see where the graph crosses the x-axis; that will be the real solution. Note that the graph crosses the x-axis at one place: 0.762831450377. This means that 0.762831450377 is the real solution.
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