SOLUTION: URGENT CAN SOMEONE HELP ME ON THIS PROBLEM BY COMPLETING THE SQUARE 5x^2-2x=7

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: URGENT CAN SOMEONE HELP ME ON THIS PROBLEM BY COMPLETING THE SQUARE 5x^2-2x=7      Log On


   

Question 693848: URGENT CAN SOMEONE HELP ME ON THIS PROBLEM
BY COMPLETING THE SQUARE
5x^2-2x=7
Found 2 solutions by Alan3354, mouk:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2-2x=7
Divide by 5 to make the coefficient of x^2 = 1
x%5E2+-+%282%2F5%29x+=+7%2F5
a = 1, b = -2/5
Add (b/2)^2 = 1/25
x%5E2+-+%282%2F5%29x+%2B1%2F25+=+7%2F5+%2B+1%2F25
x%5E2+-+%282%2F5%29x+%2B1%2F25+=+36%2F25
%28x+-+1%2F5%29%5E2+=+%286%2F5%29%5E2
x - 1/5 = ± 6/5
======================
x = 1/5 + 6/5 = 7/5
----------
x = 1/5 - 6/5 = -1

Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
+5x%5E2-2x-7=0+
Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form


y=5+x%5E2-2+x%2B7 Start with the given equation



y-7=5+x%5E2-2+x Subtract 7 from both sides



y-7=5%28x%5E2%2B%28-2%2F5%29x%29 Factor out the leading coefficient 5



Take half of the x coefficient -2%2F5 to get -1%2F5 (ie %281%2F2%29%28-2%2F5%29=-1%2F5).


Now square -1%2F5 to get 1%2F25 (ie %28-1%2F5%29%5E2=%28-1%2F5%29%28-1%2F5%29=1%2F25)





y-7=5%28x%5E2%2B%28-2%2F5%29x%2B1%2F25-1%2F25%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 1%2F25 does not change the equation




y-7=5%28%28x-1%2F5%29%5E2-1%2F25%29 Now factor x%5E2%2B%28-2%2F5%29x%2B1%2F25 to get %28x-1%2F5%29%5E2



y-7=5%28x-1%2F5%29%5E2-5%281%2F25%29 Distribute



y-7=5%28x-1%2F5%29%5E2-1%2F5 Multiply



y=5%28x-1%2F5%29%5E2-1%2F5%2B7 Now add 7 to both sides to isolate y



y=5%28x-1%2F5%29%5E2%2B34%2F5 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=5, h=1%2F5, and k=34%2F5. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=5x%5E2-2x%2B7 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C5x%5E2-2x%2B7%29 Graph of y=5x%5E2-2x%2B7. Notice how the vertex is (1%2F5,34%2F5).



Notice if we graph the final equation y=5%28x-1%2F5%29%5E2%2B34%2F5 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C5%28x-1%2F5%29%5E2%2B34%2F5%29 Graph of y=5%28x-1%2F5%29%5E2%2B34%2F5. Notice how the vertex is also (1%2F5,34%2F5).



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