Solve for x in the following equation.
Answer: are the exact answers using the Quadratic Formula.
even though the two answers look different, they are equivalent because both yield the same approximate answers of and
Simplify the equation .
Divide both sides by
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
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 1 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 6.57797305561 and one at -10.31963044.
The answers are 6.57797305561 and -10.31963044. 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 = 6.57797305561 by substituting 6.57797305561 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 6.57797305561 for x, then x = 6.57797305561 is a solution.
Check the solution x = -10.31963044 by substituting -10.31963044 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 -10.31963044 for x, then x = - 10.31963044 is a solution.
The solutions to the equation are 6.57797305561 and -10.31963044.
If you would like to review the solution to problem 4.5d, click on Problem
If you would like to go back to the beginning of the quadratic section, click on Quadratic
If you would like to go back to the equation table of contents, click on Contents
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