SOLUTION: Solve the following equation by completing the square x2-8x+15=0 Once again I'm lost!!!!

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Question 134317: Solve the following equation by completing the square
x2-8x+15=0
Once again I'm lost!!!!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form


y=1+x%5E2-8+x%2B15 Start with the given equation



y-15=1+x%5E2-8+x Subtract 15 from both sides



y-15=1%28x%5E2-8x%29 Factor out the leading coefficient 1



Take half of the x coefficient -8 to get -4 (ie %281%2F2%29%28-8%29=-4).


Now square -4 to get 16 (ie %28-4%29%5E2=%28-4%29%28-4%29=16)





y-15=1%28x%5E2-8x%2B16-16%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 16 does not change the equation




y-15=1%28%28x-4%29%5E2-16%29 Now factor x%5E2-8x%2B16 to get %28x-4%29%5E2



y-15=1%28x-4%29%5E2-1%2816%29 Distribute



y-15=1%28x-4%29%5E2-16 Multiply



y=1%28x-4%29%5E2-16%2B15 Now add 15 to both sides to isolate y



y=1%28x-4%29%5E2-1 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=4, and k=-1. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=1x%5E2-8x%2B15 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2-8x%2B15%29 Graph of y=1x%5E2-8x%2B15. Notice how the vertex is (4,-1).



Notice if we graph the final equation y=1%28x-4%29%5E2-1 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x-4%29%5E2-1%29 Graph of y=1%28x-4%29%5E2-1. Notice how the vertex is also (4,-1).



So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.