Note:
Solve for x in the following equation.
Problem 4.5d:
Answer: are the exact answers using the Quadratic Formula.
are the exact answers using the Completing the
Square Method.
Even though the two answers look different, they are equivalent because both
yield the same approximate answers of and
Solution:
Simplify the equation by simplifying the radicals.
Method 1: Factoring
The equation is not
easily factored. Therefore, we will not use this method.
Method 2: Completing the square
Add to both sides of the equation
Divide both sides 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:
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.
Method 4: Graphing
Graph the equation, (the left side of the original equation). Graph (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
0.12530322634 and one at -0.1535874976.
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 x=0.12530322634 by substituting 0.125303226341 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=-0.1535874976 by substituting -0.1535874976 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 0.12530322634 and
- 0.1535874976.
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