SOLUTION: x^2 - 13x + 36

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Question 474270: x^2 - 13x + 36
Answer by MathLover1(20850) 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%5E2-13%2Ax%2B36=0 ( notice a=1, b=-13, and c=36)





x+=+%28--13+%2B-+sqrt%28+%28-13%29%5E2-4%2A1%2A36+%29%29%2F%282%2A1%29 Plug in a=1, b=-13, and c=36




x+=+%2813+%2B-+sqrt%28+%28-13%29%5E2-4%2A1%2A36+%29%29%2F%282%2A1%29 Negate -13 to get 13




x+=+%2813+%2B-+sqrt%28+169-4%2A1%2A36+%29%29%2F%282%2A1%29 Square -13 to get 169 (note: remember when you square -13, you must square the negative as well. This is because %28-13%29%5E2=-13%2A-13=169.)




x+=+%2813+%2B-+sqrt%28+169%2B-144+%29%29%2F%282%2A1%29 Multiply -4%2A36%2A1 to get -144




x+=+%2813+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2813+%2B-+5%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2813+%2B-+5%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2813+%2B+5%29%2F2 or x+=+%2813+-+5%29%2F2


Lets look at the first part:


x=%2813+%2B+5%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=%2813+-+5%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=9 or x=4




+graph%28+500%2C+500%2C+-10%2C+30%2C+-10%2C+30%2C+x%5E2+-+13x+%2B+36%29+