in Mathematics+IQ challenge by 1 4 7

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

10 Answers

0 votes

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.

by 9 40 79
0 votes
(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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by 1 1 2
0 votes

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

by 1 1 7
0 votes
(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
by 1 2 5
0 votes

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  

                                         

                                       



by 2
0 votes

 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

by 4
0 votes

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!!

by 2
0 votes

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

by 1 4 9
0 votes

(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


by 3
0 votes
(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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