Note:
Solve for x in the following equation.
Example 1:
The equation is already set to zero.
Method 1:Factoring
The equation is not easily factored. Therefore, we will not use this method.
Method 2:Completing the square
Divide both sides of the equation 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 :
Subtract from both sides of the equation:
The exact answers are
and the approximate answers are
2.0646448.
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 exact answers are and the approximate answers are
2.0646448 .
Method 4:Graphing
Graph the left side of the equation, (formed by subtracting the right side of the original equation
from the left side of the original equation).Graph 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 two x-intercepts, one at
-3.355639 and one at 2.0646448.
The answers are -3.355639 and 2.0646448. 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=-3.355639 by substituting -3.355639 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
-3.355639 for x, then x=-3.355639 is a solution.
Check the solution x=2.0646448 by substituting -2.0646448 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 exact answers are and the approximate answers are
If you would like to test yourself by working some problems similar to this
example, click on Problem
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