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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Answer:
Approximately 6.8m
Step-by-step explanation:
We can picture this problem by drawing a rectangular prism with a width of 5m, a depth of 3m, and a height of 3.5m. To find the length from one corner of the floor to the opposite corner of the floor, we can use the pythagorean theorem and plug in the width and depth of the room for a and b:
And now we can solve for c...
c = 5.831m
Now that we have the length from corner to corner across the floor, we can use the pythagorean theorem again, this time using the length from corner to corner across the floor we just derived and the height of the room:
And now we can solve for c again...
c = 6.8m