Note:
Solve for x in the following equation.
Problem 4.4b:
Answer:
Solution:
The equation is already equal to zero.
If you have forgotten how to manipulate fractions, click on Fractions for a review.
Remove all the fractions by writing the equation in an equivalent form
without fractional coefficients. In this problem, you can do it by
multiplying both sides of the equation by 20.
Method 1:Factoring
The equation can be rewritten in the equivalent factored form of
The answers are and using the factoring
method.
Method 2:Completing the square
Subtract 4 from both sides of the equation
Divide both sides by 45:
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:
Add to both sides of the equation:
The answers are and using the method of
Completing the Square.
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 answers are and using the method of the
Quadratic Fromula.
Method 4:Graphing
Graph the equation, (the left side of the original equation). Graph (the right side of the original equation and 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
0.3333333 and one at 0.266667.
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.
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
If you would like to test yourself by working some problems similar to this
example, click on Problem
If you would like to go back to the equation table of contents, click on
Contents
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.