Solve the following quadratic equation by factoring.
2 answers:
<h3>Answer: x = -2 or x = 7 (choice D)</h3>
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Work Shown:
x^2 - 5x = 14
x^2 - 5x - 14 = 0
(x-7)(x+2) = 0 .... this step is further explained below
x-7 = 0 or x+2 = 0
x = 7 or x = -2
The order of the solutions does not matter.
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To factor x^2-5x-14, we need to find two numbers that multiply to -14 and add to -5. This is done through trial and error. I recommend making a table to help organize everything. See the diagram below.
After a bit of guess work, you should find that -7 and 2 are the two values we're after
-7 + 2 = -5
-7 * 2 = -14
This is why x^2-5x-14 = (x-7)(x+2)
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So, each cheeseburger is $4 and each lemonade is $1. The final answer is:
1 cheeseburger and 2 cups of lemonade would cost $6.
Divide the second equation by -2 to begin the process of solving by elimination:
Now that we have c, 4, we can plug it in to one of the equations to find l:
So, each cheeseburger is $4 and each lemonade is $1. The final answer is:
1 cheeseburger and 2 cups of lemonade would cost $6.
