SOLUTION: how do you slove x= y squared-14y+25

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Question 467379: how do you slove x= y squared-14y+25
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solving for y:


x=y%5E2-14y%2B25 Start with the given equation.


0=y%5E2-14y%2B25-x Subtract x from both sides.



Notice that the quadratic y%5E2-14y%2B25-x is in the form of Ay%5E2%2BBy%2BC where A=1, B=-14, and C=25-x (note: x is a constant at this point)



Use quadratic formula
y+=+%28-B%2B-sqrt%28B%5E2-4AC%29%29%2F%282A%29


y+=+%28-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2-4%281%29%2825-x%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-14, and C=25-x


y+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%281%29%2825-x%29+%29%29%2F%282%281%29%29 Negate -14 to get 14.


y+=+%2814+%2B-+sqrt%28+196-4%281%29%2825-x%29+%29%29%2F%282%281%29%29 Square -14 to get 196.


y+=+%2814+%2B-+sqrt%28+196-4%2825-x%29+%29%29%2F%282%29 Multiply


y+=+%2814+%2B-+sqrt%28+4%2849-%2825-x%29%29+%29%29%2F%282%29 Factor out the GCF 4


y+=+%2814+%2B-+sqrt%28+4+%29%2A+sqrt%28%2849-%2825-x%29%29+%29%29%2F%282%29 Break up the square root.


y+=+%2814+%2B-+2%2A+sqrt%2849-25%2Bx+%29%29%2F%282%29 Simplify


y+=+%2814+%2B-+2%2A+sqrt%28x%2B24%29%29%2F%282%29 Combine like terms and rearrange the terms.


y+=+7+%2B-+sqrt%28x%2B24%29 Reduce.


So the solution is y+=+7+%2B-+sqrt%28x%2B24%29


This is the same as saying that

y+=+7+%2B+sqrt%28x%2B24%29 or y+=+7+-+sqrt%28x%2B24%29