SOLVING QUADRATIC EQUATIONSSOLVING QUADRATIC EQUATIONS
Problem 4.5b:
The equation
Subtract 1 to both sides of the equation
The quadratic formula is
Graph the equation,
Factoring
Completing the Square
Quadratic Formula
Graphing
Solve for x in the following equation.
Answer:
are the exact answers using the Quadratic Formula.
are the exact answers using the Completing the Square
Method.
Even though the two answers look different, they are equivalent because both
yield the same approximate answers of 
and 
Solution:
Simplify the equation
by simplifying the radicals.
Eliminate the denominator 5 by multiplying both sides by 5.
Method 1:Factoring
is not easily
factored. Therefore, we will not use this method.
Method 2:Completing the square
Divide both sides by 
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 :
are
the exact answers 
are
approximate answers.
Method 3:Quadratic Formula
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.
are the
exact answers 
are
approximate answers.
Method 4:Graphing
(the left side of the original equation). Graph 
(the
x-axis). 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
-0.02354671551 and one at -1.20119815588.
The answers are -0.02354671551 and -1.20119815588. 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=-0.02354671551 by substituting -0.02354671551 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 -0.02354671551 for x,
then x=-0.02354671551 is a solution.
Check the solution x=-1.20119815588 by substituting -1.20119815588 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 -1.20119815588 for x,
then x=-1.20119815588 is a solution.
The solutions to the equation 
are-0.02354671551 and-1.20119815588.
If you would like to review the solution to problem 4.5c, click on Problem
If you would like to go back to the beginning of the quadratic section,
click on Quadratic
If you would like to go back to the equation table of contents, click on
Contents
This site was built to accommodate the needs of students. The topics and
problems are what students ask for. We ask student to help in the editing so
that future viewers will access a cleaner site. If you feel that some of the
material is this section is ambiguous or needs more clarification, please
let us know by e-mail.
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour
