SOLUTION: solve: x^2-14x+45=0 (i forgot how to solve these)

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Question 484925: solve: x^2-14x+45=0
(i forgot how to solve these)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-14%2Ax%2B45=0 ( notice a=1, b=-14, and c=45)





x+=+%28--14+%2B-+sqrt%28+%28-14%29%5E2-4%2A1%2A45+%29%29%2F%282%2A1%29 Plug in a=1, b=-14, and c=45




x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%2A1%2A45+%29%29%2F%282%2A1%29 Negate -14 to get 14




x+=+%2814+%2B-+sqrt%28+196-4%2A1%2A45+%29%29%2F%282%2A1%29 Square -14 to get 196 (note: remember when you square -14, you must square the negative as well. This is because %28-14%29%5E2=-14%2A-14=196.)




x+=+%2814+%2B-+sqrt%28+196%2B-180+%29%29%2F%282%2A1%29 Multiply -4%2A45%2A1 to get -180




x+=+%2814+%2B-+sqrt%28+16+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2814+%2B-+4%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2814+%2B-+4%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2814+%2B+4%29%2F2 or x+=+%2814+-+4%29%2F2


Lets look at the first part:


x=%2814+%2B+4%29%2F2


x=18%2F2 Add the terms in the numerator

x=9 Divide


So one answer is

x=9




Now lets look at the second part:


x=%2814+-+4%29%2F2


x=10%2F2 Subtract the terms in the numerator

x=5 Divide


So another answer is

x=5


So our solutions are:

x=9 or x=5