Note:
Solve for x in the following equation.
Example 2:
The equation is already equal to zero.
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 3 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, -5 for b, and 3 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. The x-intercepts are 4.30277563773 and
The exact answers are and The approximate answers are 4.30277563773 and
Check these answers in the original equation.
Check the solution x=4.30277563773 by substituting 4.30277563773 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=0.697224362268 by substituting 0.697224362268 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
rounded to 4.30277563773 and 0.697224362268
Comment: You can use the solutions to factor the original equation.
For example, since , then , and
Since , then , and
Since the product and , 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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Author:Nancy Marcus