SOLUTION: x^2+2x=0 what number is needed to complete the square if answer not an interger then round to nearest hundreth

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: x^2+2x=0 what number is needed to complete the square if answer not an interger then round to nearest hundreth      Log On


   

Question 474662: x^2+2x=0 what number is needed to complete the square if answer not an interger then round to nearest hundreth
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%2B2+x%2B0 Start with the given equation



y-0=1+x%5E2%2B2+x Subtract 0 from both sides



y-0=1%28x%5E2%2B2x%29 Factor out the leading coefficient 1



Take half of the x coefficient 2 to get 1 (ie %281%2F2%29%282%29=1).


Now square 1 to get 1 (ie %281%29%5E2=%281%29%281%29=1)





y-0=1%28x%5E2%2B2x%2B1-1%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 1 does not change the equation




y-0=1%28%28x%2B1%29%5E2-1%29 Now factor x%5E2%2B2x%2B1 to get %28x%2B1%29%5E2



y-0=1%28x%2B1%29%5E2-1%281%29 Distribute



y-0=1%28x%2B1%29%5E2-1 Multiply



y=1%28x%2B1%29%5E2-1%2B0 Now add 0 to both sides to isolate y



y=1%28x%2B1%29%5E2-1 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=1, h=-1, 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%2B2x%2B0 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2%2B2x%2B0%29 Graph of y=1x%5E2%2B2x%2B0. Notice how the vertex is (-1,-1).



Notice if we graph the final equation y=1%28x%2B1%29%5E2-1 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x%2B1%29%5E2-1%29 Graph of y=1%28x%2B1%29%5E2-1. Notice how the vertex is also (-1,-1).



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