SOLUTION: Give exaxt and approximate sollutions to three decimal places... y^2 - 10y + 25=16

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Question 266157: Give exaxt and approximate sollutions to three decimal places... y^2 - 10y + 25=16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y%5E2-10y%2B25=16 Start with the given equation.


y%5E2-10y%2B25-16=0 Subtract 16 from both sides.


y%5E2-10y%2B9=0 Combine like terms.


Notice that the quadratic y%5E2-10y%2B9 is in the form of Ay%5E2%2BBy%2BC where A=1, B=-10, and C=9


Let's use the quadratic formula to solve for "y":


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


y+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-10, and C=9


y+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%289%29+%29%29%2F%282%281%29%29 Negate -10 to get 10.


y+=+%2810+%2B-+sqrt%28+100-4%281%29%289%29+%29%29%2F%282%281%29%29 Square -10 to get 100.


y+=+%2810+%2B-+sqrt%28+100-36+%29%29%2F%282%281%29%29 Multiply 4%281%29%289%29 to get 36


y+=+%2810+%2B-+sqrt%28+64+%29%29%2F%282%281%29%29 Subtract 36 from 100 to get 64


y+=+%2810+%2B-+sqrt%28+64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%2810+%2B-+8%29%2F%282%29 Take the square root of 64 to get 8.


y+=+%2810+%2B+8%29%2F%282%29 or y+=+%2810+-+8%29%2F%282%29 Break up the expression.


y+=+%2818%29%2F%282%29 or y+=++%282%29%2F%282%29 Combine like terms.


y+=+9 or y+=+1 Simplify.


So the solutions are y+=+9 or y+=+1