Note:
Solve for x in the following equation.
Example 4:
The equation is already set to zero.
Simplify the equation.
Method 1:Factoring
The equation is not easily factored. Therefore, we will not use this method.
Method 2:Completing the square
Add to both sides of the equation .
Divide both sides of the equation by and simplify.
Add to both sides of the equation:
Factor the left side and simplify the right side:
Take the square root of both sides of the equation:
Subtract from both sides of the equation:
The exact answers are and the approximate answers are
Method 3:Quadratic Formula
The quadratic formula is
In the equation ,a is
the coefficient of the term, b is the coefficient of the x
term, and c is the constant. Substitute for a, for b, and for c in the quadratic formula and simplify.
The exact answers are and the approximate answers are
Method 4:Graphing
Graph the left side of the equation, Graph is nothing more
than the x-axis. So what you will be looking for is where the graph of crosses the x-axis. Another way of
saying this is that the x-intercepts are the solutions to this equation.
You can see from the graph that there are two x-intercepts, one at 2.7616977 and one at -3.710381013.
The answers are 2.7616977 and -3.710381013. These answers may or
may not be solutions to the original equations. You must verify that these
answers are solutions.
Check these answers in the original equation.
Check the solution x=2.7616977 by substituting 2.7616977 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.
Check the solution x=-3.710381013 by substituting -3.710381013 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.
The exact answers are and the approximate answers are
If you would like to test yourself by working some problems similar to this
example, click on Problem
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