SOLUTION: Use the quadratic formula to solve the following equations x^2 - 22x + 121 = 0

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Question 101332: Use the quadratic formula to solve the following equations
x^2 - 22x + 121 = 0
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%5E2-22%2Ax%2B121=0 ( notice a=1, b=-22, and c=121)





x+=+%28--22+%2B-+sqrt%28+%28-22%29%5E2-4%2A1%2A121+%29%29%2F%282%2A1%29 Plug in a=1, b=-22, and c=121




x+=+%2822+%2B-+sqrt%28+%28-22%29%5E2-4%2A1%2A121+%29%29%2F%282%2A1%29 Negate -22 to get 22




x+=+%2822+%2B-+sqrt%28+484-4%2A1%2A121+%29%29%2F%282%2A1%29 Square -22 to get 484 (note: remember when you square -22, you must square the negative as well. This is because %28-22%29%5E2=-22%2A-22=484.)




x+=+%2822+%2B-+sqrt%28+484%2B-484+%29%29%2F%282%2A1%29 Multiply -4%2A121%2A1 to get -484




x+=+%2822+%2B-+sqrt%28+0+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2822+%2B-+0%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2822+%2B-+0%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2822+%2B+0%29%2F2 or x+=+%2822+-+0%29%2F2


Lets look at the first part:


x=%2822+%2B+0%29%2F2


x=22%2F2 Add the terms in the numerator

x=11 Divide


So one answer is

x=11




Now lets look at the second part:


x=%2822+-+0%29%2F2


x=22%2F2 Subtract the terms in the numerator

x=11 Divide


So another answer is

x=11


So our solutions are:

x=11 or x=11


which means we only have one solution


x=11






So this means that the only solution is x=11