Note:
Solve for x in the following equation.
Problem 4.4c:
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 8.
Method 1:Factoring
The equation is not easily factored. Therefore, we will not use this method.
Method 2:Completing the square
Subtract 192 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:
Subtract 7 from both sides of the equation:
The answers are and
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
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 no x-intercepts. This means that
there are no real answers; the answers are imaginary.
The answers are 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
Comment:You can use the exact solutions to factor the left side of the
original equation minus the right side of the original equation:
Since
Since
The product
Since and
then we could say
However the product of the first terms of the factors does not equal
Multiply
by
Let s check to see if
The factors of
are , and
If you would like to test yourself by working some problems similar to this
example, click on Problem
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on Contents
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