Note:
Solve for x in the following equation.
Example 1:
The equation is already set to zero.
Method 1: Factoring
Method 2: Completing the square
Divide both sides of the equation by 2.
Add to 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. Substitute 2 for a, -1 for b, and -1 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.
You can see from the graph that there are two x-intercepts, one at 1 and one at .
The answers are 1 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 x=1 by substituting 1 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 1 and
If you would like to work another example, click on Example.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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Contents.
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