Note:
Solve for x in the following equation.
Example 2:
The equation is already set to zero.
Simplify the equation.
can be rewritten as:
Method 1:Factoring
The equation is not easily factored. Therefore, we will not use this method.
Method 2:Completing the square
Add 8 to both sides of the equation .
Divide both sides of the equation by and 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:
Subtract from both sides of the equation:
The exact answers are and the approximate answers are
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 -8 for c in
the quadratic formula and simplify.
The exact answers are and the approximate answers are
Method 4:Graphing
Graph the left side of the equation,
Graph 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
0.77292396 and one at -2.439590637.
The answers are 0.77292396 and -2.43950637. 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=0.77292396 by substituting 0.77292396 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 x=-2.439590637 by substituting -2.439590637 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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