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

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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)   (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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Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

1.


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


Start with the given equation



Subtract from both sides



Factor out the leading coefficient



Take half of the x coefficient to get (ie ).


Now square to get (ie )





Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation




Now factor to get



Distribute



Multiply



Now add to both sides to isolate y



Combine like terms




Now the quadratic is in vertex form where , , and . Remember (h,k) is the vertex and "a" is the stretch/compression factor.




Check:


Notice if we graph the original equation we get:


Graph of . Notice how the vertex is (,).



Notice if we graph the final equation we get:


Graph of . Notice how the vertex is also (,).



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






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