Q) how to solve by completing the square method ? a) 2x^2+16x+52x2+16x+5 b) 6+4x-x^26+4x−x2

2 Answers
kubik98
Dec 25, 2017

a) 2(x+2)^2-32(x+2)2−3

b) 10-(x-2)^210−(x−2)2

Explanation:

a) 2x^2+16x+52x2+16x+5

=>2[x^2+8x+5/2]⇒2[x2+8x+52]

(color(red)a+color(blue)b)^2=a^2+color(green)2color(red)acolor(blue)b+b^2(a+b)2=a2+2ab+b2

=>2[color(red)x^2+color(green)2*color(blue)4color(red)x+color(blue)4^2-4^2+5/2]⇒2[x2+2⋅4x+42−42+52]

=>2[(color(red)x^2+color(green)2*color(blue)4color(red)x+color(blue)4^2)-16+5/2]⇒2[(x2+2⋅4x+42)−16+52]

=>2[(x+4)^2-32/2+5/2]⇒2[(x+4)2−322+52]

=>2[(x+4)^2-27/2]⇒2[(x+4)2−272]

=>2(x+4)^2-cancel2*27/cancel2

=>2(x+4)^2-27

b) 6+4x−x^2

=>-1*[x^2-4x-6]

=>-1*[color(red)x^2-color(green)2*color(blue)2color(red)x+color(blue)2^2-2^2-6]

=>-1*[(color(red)x^2-color(green)2*color(blue)2color(red)x+color(blue)2^2)-4-6]

=>-1*[(color(red)x-color(blue)2)^2-10]

=>-(x-2)^2+10

=>10-(x-2)^2

P dilip_k
Dec 25, 2017

Assuming that we are to solve the equations completing the square method.

a) 2x^2+16x+5=0

=>x^2+8x+5/2=0

=>x^2+2*x*4+4^2-4^2+5/2=0

=>(x+4)^2-16+5/2=0

=>(x+4)^2-27/2=0

=>(x+4)^2=27/2

=>x+4=pmsqrt27/2

=>x=-4pm(3sqrt3)/2

(b) 6+4x-x^2=0

=>6+2^2-2^2+2*x*2-x^2=0

=>10-(2^2-2*x*2+x^2)=0

=>(x-2)^2 =10

=>x-2 =pmsqrt10

=>x=2pmsqrt10

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