SOLUTION: Solve by using the quadratic formula. x^2 – 9x + 20 = 0

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Question 103588: Solve by using the quadratic formula. x^2 – 9x + 20 = 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%5E2-9%2Ax%2B20=0 ( notice a=1, b=-9, and c=20)





x+=+%28--9+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A20+%29%29%2F%282%2A1%29 Plug in a=1, b=-9, and c=20




x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A20+%29%29%2F%282%2A1%29 Negate -9 to get 9




x+=+%289+%2B-+sqrt%28+81-4%2A1%2A20+%29%29%2F%282%2A1%29 Square -9 to get 81 (note: remember when you square -9, you must square the negative as well. This is because %28-9%29%5E2=-9%2A-9=81.)




x+=+%289+%2B-+sqrt%28+81%2B-80+%29%29%2F%282%2A1%29 Multiply -4%2A20%2A1 to get -80




x+=+%289+%2B-+sqrt%28+1+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%289+%2B-+1%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%289+%2B-+1%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%289+%2B+1%29%2F2 or x+=+%289+-+1%29%2F2


Lets look at the first part:


x=%289+%2B+1%29%2F2


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

x=5 Divide


So one answer is

x=5




Now lets look at the second part:


x=%289+-+1%29%2F2


x=8%2F2 Subtract the terms in the numerator

x=4 Divide


So another answer is

x=4


So our solutions are:

x=5 or x=4