SOLUTION: Please help, it asks to solve by completing the square. the problem is: 2x^-3x+1=0, the answer that I got for this was 1 - 2 Please help, thank you=)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help, it asks to solve by completing the square. the problem is: 2x^-3x+1=0, the answer that I got for this was 1 - 2 Please help, thank you=)       Log On


   

Question 131146: Please help, it asks to solve by completing the square. the problem is:
2x^-3x+1=0, the answer that I got for this was
1
-
2
Please help, thank you=)

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=2+x%5E2-3+x%2B1 Start with the given equation



y-1=2+x%5E2-3+x Subtract 1 from both sides



y-1=2%28x%5E2%2B%28-3%2F2%29x%29 Factor out the leading coefficient 2



Take half of the x coefficient -3%2F2 to get -3%2F4 (ie %281%2F2%29%28-3%2F2%29=-3%2F4).


Now square -3%2F4 to get 9%2F16 (ie %28-3%2F4%29%5E2=%28-3%2F4%29%28-3%2F4%29=9%2F16)





y-1=2%28x%5E2%2B%28-3%2F2%29x%2B9%2F16-9%2F16%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 9%2F16 does not change the equation




y-1=2%28%28x-3%2F4%29%5E2-9%2F16%29 Now factor x%5E2%2B%28-3%2F2%29x%2B9%2F16 to get %28x-3%2F4%29%5E2



y-1=2%28x-3%2F4%29%5E2-2%289%2F16%29 Distribute



y-1=2%28x-3%2F4%29%5E2-9%2F8 Multiply



y=2%28x-3%2F4%29%5E2-9%2F8%2B1 Now add 1 to both sides to isolate y



y=2%28x-3%2F4%29%5E2-1%2F8 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=2, h=3%2F4, and k=-1%2F8. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=2x%5E2-3x%2B1 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C2x%5E2-3x%2B1%29 Graph of y=2x%5E2-3x%2B1. Notice how the vertex is (3%2F4,-1%2F8).



Notice if we graph the final equation y=2%28x-3%2F4%29%5E2-1%2F8 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C2%28x-3%2F4%29%5E2-1%2F8%29 Graph of y=2%28x-3%2F4%29%5E2-1%2F8. Notice how the vertex is also (3%2F4,-1%2F8).



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