Completing the square is as easy as it sounds !
Let's consider the equation: " x^2+6x+2=0 "
The first step in completing the square is is moving the constant term, which in this case is 2, to the other side of the equation. The equation now looks like: " x^2+6x+__= -2 "
The second step is to take the coefficient of the middle term, which is 6 in this case, and dividing it in half and squaring it. So 6 divided in half is 3. 3 squared is 9.
The third step is to add 9 to both sides of the equation. " x^2+6x+9 = -2+9 "
simplified to : x^2 + 6x + 9 = 7
The fourth step is to factor the trinomial : (x+3)^2 = 7
The next step is to find the square root of both sides : The square root of (x+3)^2 is (x+3) .
The square root of 7 can be either negative or positive , so its written like: +-√7
The last step is to subtract 3 from each side : (x+3) = +- √7
- 3 - 3
The final answer you get is : x= -3 +- √7
Now You Try It :
x^2 + 8x + ___ = 7
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