SOLUTION: Hello Tutors, For some reason I can not figure these things out! I know that the Quadratic Formula is: x = -b±√b2 – 4ac / 2a But I can't get plugging the problem x^2 -

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello Tutors, For some reason I can not figure these things out! I know that the Quadratic Formula is: x = -b±√b2 – 4ac / 2a But I can't get plugging the problem x^2 -      Log On


   

Question 103812This question is from textbook Intermediate Algebra
: Hello Tutors,
For some reason I can not figure these things out! I know that the Quadratic Formula is:
x = -b±√b2 – 4ac / 2a
But I can't get plugging the problem x^2 - 3x = 7x -2 into the formula and solve. Can someone please help?????
Further directions from my 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.
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+-+3x+=+7x+-2 Start with the given equation


+x%5E2+-+3x+-7x%2B2=0 Get all terms to one side


+x%5E2+-+10x%2B2=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%5E2-10%2Ax%2B2=0 ( notice a=1, b=-10, and c=2)





x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Plug in a=1, b=-10, and c=2




x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Negate -10 to get 10




x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A2+%29%29%2F%282%2A1%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)




x+=+%2810+%2B-+sqrt%28+100%2B-8+%29%29%2F%282%2A1%29 Multiply -4%2A2%2A1 to get -8




x+=+%2810+%2B-+sqrt%28+92+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2810+%2B-+2%2Asqrt%2823%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2810+%2B-+2%2Asqrt%2823%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2810+%2B+2%2Asqrt%2823%29%29%2F2 or x+=+%2810+-+2%2Asqrt%2823%29%29%2F2



Now break up the fraction



x=%2B10%2F2%2B2%2Asqrt%2823%29%2F2 or x=%2B10%2F2-2%2Asqrt%2823%29%2F2



Simplify



x=5%2Bsqrt%2823%29 or x=5-sqrt%2823%29



So the solutions are:

x=5%2Bsqrt%2823%29 or x=5-sqrt%2823%29