Note:
Solve for x in the following equation.
Example 1:
Set the equation equal to zero by subtracting 3 x and 7 from both sides of the equation.
Method 1: Factoring
The left side of the equation is not easily factored, so we will not use this method.
Method 2: Completing the Square
Subtract 15 from both sides of the equation .
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:
Add to both sides of the equation:
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. Simply insert 1 for a, -3
for b, and 15 for c in the quadratic formula and
simplify.
Method 4: Graphing
Graph y= the left side of the equation or and graph y= the right side of the equation or y=0. The graph of y=0 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 no x-intercepts. This means that
there are no real answers; the solution are two imaginary numbers.
The answers are and
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 by substituting 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.
Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value
for x, then
is a solution.
Check the solution by substituting
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 solutions to the equation are and
Comment: You can use the solutions to factor the original equation.
For example, since ,then
Since , then
Since the product
then we can say that
This means that
and
are factors of
If you would like to test yourself by working some problems similar to this
example, click on Problem.
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Contents.
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