SOLUTION: Completing the square. This is so difficult. Can someone show me easy steps to understand this. 1.)4x^2+x+3=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Completing the square. This is so difficult. Can someone show me easy steps to understand this. 1.)4x^2+x+3=0       Log On


   

Question 715877: Completing the square. This is so difficult. Can someone show me easy steps to understand this.
1.)4x^2+x+3=0
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Step 1: Divide through by the lead coefficient.




Step 2: Add the opposite of the constant term to both sides.



Step 3: Divide the coefficient on the first degree term by 2, square the result, and then add that result to both sides of the equation.



Step 4: The result of step 3 is a perfect square trinomial in the LHS. Factor it.



Step 5: Take the square root of both sides. Remember to consider both positive and negative roots.



Step 6: Add the opposite of the constant term in the LHS to both sides:



John

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My calculator said it, I believe it, that settles it
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.
4x%5E2%2Bx%2B3=0

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


y=4+x%5E2%2B1+x%2B3 Start with the given equation



y-3=4+x%5E2%2B1+x Subtract 3 from both sides



y-3=4%28x%5E2%2B%281%2F4%29x%29 Factor out the leading coefficient 4



Take half of the x coefficient 1%2F4 to get 1%2F8 (ie %281%2F2%29%281%2F4%29=1%2F8).


Now square 1%2F8 to get 1%2F64 (ie %281%2F8%29%5E2=%281%2F8%29%281%2F8%29=1%2F64)





y-3=4%28x%5E2%2B%281%2F4%29x%2B1%2F64-1%2F64%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 1%2F64 does not change the equation




y-3=4%28%28x%2B1%2F8%29%5E2-1%2F64%29 Now factor x%5E2%2B%281%2F4%29x%2B1%2F64 to get %28x%2B1%2F8%29%5E2



y-3=4%28x%2B1%2F8%29%5E2-4%281%2F64%29 Distribute



y-3=4%28x%2B1%2F8%29%5E2-1%2F16 Multiply



y=4%28x%2B1%2F8%29%5E2-1%2F16%2B3 Now add 3 to both sides to isolate y



y=4%28x%2B1%2F8%29%5E2%2B47%2F16 Combine like terms




Now the quadratic is in vertex form y=a%28x-h%29%5E2%2Bk where a=4, h=-1%2F8, and k=47%2F16. Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation y=4x%5E2%2B1x%2B3 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4x%5E2%2B1x%2B3%29 Graph of y=4x%5E2%2B1x%2B3. Notice how the vertex is (-1%2F8,47%2F16).



Notice if we graph the final equation y=4%28x%2B1%2F8%29%5E2%2B47%2F16 we get:


graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4%28x%2B1%2F8%29%5E2%2B47%2F16%29 Graph of y=4%28x%2B1%2F8%29%5E2%2B47%2F16. Notice how the vertex is also (-1%2F8,47%2F16).



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