x(x+1)=56 solve using completing the square method
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x^2+3x+1=0
Answer:
The roots are
x1=−3+√52 and x1=−3−√52
Explanation:
From the given x2+3x+1=0, we can see that the coefficient of x^2 is already 1, so we can begin with the coefficient of x which is 3.
The 3 will have to be divided by 2 then the result should be squared and the final result is 94. This number will be added and subtracted in the equation on one side.
x2+3x+1=0
x2+3x+94−94+1=0
The first 3 terms now will form a PST-perfect square trinomial.
x2+3x+94−94+1=0
(x2+3x+94)−94+1=0
this (x2+3x+94) is equivalent to (x+32)2
So, the equation becomes
(x+32)2−94+1=0
simplify
(x+32)2−54=0
transpose the 5/4 to the right side
(x+32)2=54
Extract the square root of both sides of the equation
√(x+32)2=√54
x+32=±√52
x=−32±√52
The roots are
x1=−3+√52 and x1=−3−√52
God bless....I hope the explanation is useful.
you can also solve your sum in similar way.
Answer:
The roots are
x1=−3+√52 and x1=−3−√52
Explanation:
From the given x2+3x+1=0, we can see that the coefficient of x^2 is already 1, so we can begin with the coefficient of x which is 3.
The 3 will have to be divided by 2 then the result should be squared and the final result is 94. This number will be added and subtracted in the equation on one side.
x2+3x+1=0
x2+3x+94−94+1=0
The first 3 terms now will form a PST-perfect square trinomial.
x2+3x+94−94+1=0
(x2+3x+94)−94+1=0
this (x2+3x+94) is equivalent to (x+32)2
So, the equation becomes
(x+32)2−94+1=0
simplify
(x+32)2−54=0
transpose the 5/4 to the right side
(x+32)2=54
Extract the square root of both sides of the equation
√(x+32)2=√54
x+32=±√52
x=−32±√52
The roots are
x1=−3+√52 and x1=−3−√52
God bless....I hope the explanation is useful.
you can also solve your sum in similar way.
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