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Question 137262: how do you complete the square? x^2+10x+24=0
Answer by MORUPHOSUOLALE(24)  (Show Source):
You can put this solution on YOUR website! how do you complete the square? x^2+10x+24=0
To solve this by completing the square method!
x^2+10x+24=0
First thing is to apply any properties to cancel the constant term (24) on the left side of the equation.
A property that came to mind and which is the best - is to subtract the constant (24) from both sides of the equation.
We don't want the constant term on the left side of the equation as a process of completing the square method! (that is always the first step).
Therefore by subtracting 24 from both sides of the equation.The equation becomes- x^2+10x+24-24= 0-24
x^2+10x = -24
The second step is to... find the constant term that makes the left side a perfect square trinomial by squaring half the coefficient of x. Add this constant to both sides of the equation.(This statement might be a little bit confusing but endeavor to sit down and make sense of it by reading it carefully and apply it)-The statement is no mistake at all.
Okay lets apply step 2 rule-
half of 10(co-efficient of x) is 5 and (5)^2 = 25.1.e (by squaring half the coefficient of x )
Add this 25 to both sides of the equation...
x^2+10x = -24
x^2+10x+25 = -24+25
(x+5)(x+5) = 1
(x+5)^2 = 1
(x+5) = sqrt(1))
x+5 = +1 OR - 1
x+5= +1
x= 1-5 = -4
OR
x+5 = -1
x= -1-5
x= -6
The solutions are ... x= -6 or x= -4
Following those steps,you should be fine.
Completing the square is the longest and most complicating approach of solving a quadratic equation.
No one would prefer to use this method because of its complication,this is the reason why most instructors will categorically instruct student to use it without giving them any other options such as factorization or almighty fomulae.
To verify this -lets use factorization method and you will see that factorization might be as effective in solving some quadratic equation but require lesser amount of time and energy.
Ok lets see fatctorization...
x^2+10x+24=0
by factorization--
(x+6)(x+4)= 0
x= -6 OR -4
U see very easy and as effective as getting the same answer like the completing the square method!
I hope this helps
Moruph Osuoale
mosuolal@uncc.edu
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