SOLUTION: Hello Tutors, Here is another Quadratic formula problem I seriously need your help on. Directions from the Professor are as follows; Make sure that your work is demonstrating

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Question 103815This question is from textbook Intermediate Algebra
: Hello Tutors,
Here is another Quadratic formula problem I seriously need your help on.
Directions from the Professor are as follows;
Make sure that your work is demonstrating the solving method given in the instructions. Use the Insert and Symbols menus in Word to present the radical √ and plus/minus ± symbols. Remember that radicands must be enclosed within [ ]. Typing your work vertically is preferred but optional. If you choose to type horizontally, make sure you are appropriately using grouping symbols.
Here is the Problem:
Solve by using the Quadratic Formula;
x^2 - 7x - 1 + -7 Thank You! This question is from textbook Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+7x+-+1+%2B+-7=0 Start with the given equation


x%5E2+-+7x+-+8=0 Combine like terms


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-7%2Ax-8=0 ( notice a=1, b=-7, and c=-8)





x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Plug in a=1, b=-7, and c=-8




x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Negate -7 to get 7




x+=+%287+%2B-+sqrt%28+49-4%2A1%2A-8+%29%29%2F%282%2A1%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)




x+=+%287+%2B-+sqrt%28+49%2B32+%29%29%2F%282%2A1%29 Multiply -4%2A-8%2A1 to get 32




x+=+%287+%2B-+sqrt%28+81+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%287+%2B-+9%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%287+%2B-+9%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%287+%2B+9%29%2F2 or x+=+%287+-+9%29%2F2


Lets look at the first part:


x=%287+%2B+9%29%2F2


x=16%2F2 Add the terms in the numerator

x=8 Divide


So one answer is

x=8




Now lets look at the second part:


x=%287+-+9%29%2F2


x=-2%2F2 Subtract the terms in the numerator

x=-1 Divide


So another answer is

x=-1


So our solutions are:

x=8 or x=-1