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Solving for X in this equation would be as follows:

  1. Move all terms to the left side and set equal to zero.
  2. Now set each factor equal to zero.
Your answer:

x = 10,-22

21 Answers

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To find the value of (x+6)(x+6) = 256, you first need to simplify the left hand side of the equation:

(x+6)(x+6) = x2 +6x +6x + 36 = x2 + 12x + 36

Substituting this to the original equation will give you this x2 + 12x + 36 = 256, which can further be simplified by moving all terms to the left. Doing that will give you the quadratic form (ax2 + b2 + c = 0) of the equation:

x2 + 12x - 220 = 0

Remember that the roots can be obtained by using the quadratic formula given by:

x = [(-b)±√b2-(4ac)] / 2a where a, b, c are the coefficients of the equation. That is, a = 1, b = 12 and c = -220

Substituting the values will give you:

x = [-(12)±√(12)2-(4*1*-220)] / 2(1)

x = [-12±√144-(-880)] / 2

x = [-12±√1024] / 2

x = [-12±32] / 2

First root now equals to:
x = [-12+32] / 2
x = 10

Second root:
x = [-12-32] / 2
x = -22

There you have it. The values of x are 10 and -22.

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(x+6)(x+6)=256

take sqr root of each side

 x+6=16

x= 16 - 6

x= 10

x+6= -16

x=  -16 -6

x= -22

we find two answers x= 10  and  x= -22

                    
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The Value of x in the equation (x+6)(x+6)=256

(x+6)(x+6)=256

X2+6x+6x+36=256

X2+12X+36=256

(X+6)2=256 {(a+b)2=a2+2ab+b2}

X+6=16 (take sqr root)

X=16-6

X=10

Ans: X=10

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(X+6)(X+6)=256

(X+6)^2=256

(X+6)= 256^(1/2)

X+6=+16

X=22

And

X+6=-16

X=-10

You can also solve by making the quadratic equation and solve for that equation.
Any square root have a two solution
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let assume t = x+6

(x+6)(x+6) = 256 => t*t = 256

                                  t2  = 256 

                                         t    =  + or - 16

x + 6 = +16 => x = 10   and x + 6 = -16 => x = -22

x have two values +10 and -22  

                                         

                                       



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 Hi!

I have explained the answer in details with step by step procedure as an image file. I think this must help to you to understand clearly.image

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Simple approach to solve this :


(x+6)(x+6)=256

(x+6)2 = 256

(x+6)2 = 162


therefore, (x+6) = 16 or (x+6) = -16

Let's solve x+6=16 

=> x = 16-6 =10

Now, Lets solve x+6=-16

=>x= -16-6 = -22


therefore x = 10 ,-22 for given equation!!

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Given that:

(x + 6)(x + 6) = 256 


= (x + 6)2 = 256 


Taking square root on both the sides,


= (x + 6) = (+-)16


Hence two values for x possible,


Case 1: 

 x + 6 = 16 ==> x = 16 - 6 = 10 ==> x = 10


Case 2:

x + 6 = -16 ==> x = -16 - 6 = -22 ==> x = -22


Hence, x = 10, -22

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(x+6)(x+6)=256

or, (x+6)2 = 256

or, (x+6)= under root (256)

or, (x+6) = +16 or - 16


If x= +16, then, 

x+6=16

or,

x= 16-6=10


If x=-16, then, 

x+6=  -16

or, x= - 16-6= -22


Means, x has two values... x=10, -22


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(x+6)(x+6)=256

=>(x+6)=16 or -16 (take square roots out)

First case

(x+6)=16

=> x = 16-6 = 10

Second case 

(x+6) = -16

=> x = -16-6 = -22

So,  x can be of two values i,e 10 & -22
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(X+6)(X+6)=256

(X+6)2 =256

(X+6)2 =(16)2 or (-16)2 

Square root on both side

X+6=16  or -16

X=16-6 or -16-6

X=10 or -22.


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Given (X+6) (X+6) =256

This implies that   (X+6) ² =256

Taking square root both sides 

√(X+6 ) ² =√256

X+6 =16

X=16 −6

X=10
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(x+6)(x+6) = 256

1. Move all terms to the left side and set equals to zero.

[(x+6)(x+6)] - 256 = 0

(x+6)^2 - (16)^2 = 0

a^2 - b^2 = (a + b)(a - b)

a = x+6 and b= 16

so

(x+6+16)(x+6-16) = 0

2. Now set each factor equal to zero

x+6+16 = 0 and x+6-16 = 0

Therefore

x = - 22 and x = 10
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To solve: (x+6)(x+6) = 256

Multiply the two terms on left hand side, it becomes,

X^2 + 6x + 6x+ 36 = 256

Then,  moves all terms to left hand side,

X^2 +12x - 220= 0

X^2  + (22-10)x - 220 =0

X^2 + 22x - 10x -220 =0

x(x+22) - 10(x+22) =0

(x+22)(x-10) = 0

Equate both factors to zero,

Either, x+ 22= 0

            x =-22

Or,  x-10= 0

        x= 10

Therefore, x = -22 and 10
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Given: (x+6)(x+6) = 256

To find: value of X

Calculations : 

                       

           (x+6)(x+6) = 256

             

            by applying square root on each side we get,

                x+6 = 16

 

                 x = 16 - 6

                 x  = 10 

          

 

        
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Answer x = 10

Solving is= (x+6)(x+6)=256 is still the same as

(x+6)^2=256 and

x+6=√256 

x+6=16

Therefore x will be = 16-6 and that is = 10
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(x+6)(x+6)=256

This is the question

x^2+36=256

By multiplying both brackets we get this answer

x^2=256-36

taking 36 from right to left + becomes -

x^2=220

subtracting

x=220/2

taking the divide or right side number we get this

x=110

thats it
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X = 14

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The value of X in the equation (x+6)(x+6) is 256. Because 6 represents the addition of six parts, and x represents the addition of one part.
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(x + 6)(x + 6) = x(x + 6) + 6(x + 6) = x^2 + 12x + 36

Now we can substitute this expression into the original equation:

x^2 + 12x + 36 = 256

Subtracting 256 from both sides, we get:

x^2 + 12x - 220 = 0

To solve for x, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 12, and c = -220. Substituting these values into the formula, we get:

x = (-12 ± sqrt(12^2 - 4(1)(-220))) / 2(1)

Simplifying, we get:

x = (-12 ± sqrt(144 + 880)) / 2

x = (-12 ± sqrt(1024)) / 2

x = (-12 ± 32) / 2

Therefore, the solutions for x are:

x = (-12 + 32) / 2 = 10


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