Question

Which of the following is a solution of the equation x( x-2)/2 =24 ?

Answer 1

Step-by-step explanation:

steps using factoring by grouping-

{x(x-2)/2} = 24

= (x^2-2x)/2 = 24

= x^2-2x = 24×2 = 48

= x^2-2x-48 = 0

= x^2-8x+6x-48 = 0

= x(x-8) +6(x-8) = 0

= (x+6)(x-8) = 0

so x+6= 0

= x= 0-6=-6

and x-8=0

= x= 0+8 = 8

so x= -6,8

so the solution of the equation x( x-2)/2 =24 = -6,8

steps using quadratic formula-

x= {-b(+-) √ b^2-4ac}/a

x= {-(-2) (+-)√(-2)^2 -4(1×48)}/2

x= {2(+-)√4-4(48)}/2

x= {2(+-)√4-(-192)}/2

x= {2(+-)√4+192}/2

x= {2(+-)√196}/2

x= {2(+-)14}/2

so x= (2+14)/2 = 16/2 = 8

and x= (2-14)/2 = -12/2 = -6

so x= 8,-6

so the solution of the equation x( x-2)/2 =24 = -6,8

so the solution of the equation x( x-2)/2 =24 = -6,8

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