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Solve for x: `(4x - 2)^2 - 5 = 11` Enter the two solutions in simplified form separated...

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted September 18, 2013 at 5:24 AM via web

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Solve for x: `(4x - 2)^2 - 5 = 11`

Enter the two solutions in simplified form separated by a comma.

(4x - 2)^2 - 5 = 11

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted September 18, 2013 at 5:37 AM (Answer #1)

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To solve: `(4x - 2)^2 - 5 = 11` first remove the brackets so that a trinomial can be created:

`(4x - 2)^2 - 5 = 11`    becomes `16x^2-16x+4 -5 -11=0`  

`therefore 16x^2-16x-12=0` Simplify by dividing by 4:

`therefore 4x^2-4x-3=0`

Use the factors of 4 ( in this case `2 times 2` will be appropriate) and the factors of -3 (ie `1 times -3` in this instance) to solve:

`therefore (2x+1)(2x-3) =0`  Each factor =0

`therefore 2x=-1`

`therefore x= -1/2 `     and `2x-3=0`

`therefore x=3/2`

Ans: From `(4x - 2)^2 - 5 = 11`   x=-1/2   and x= 3/2

`x: -1/2, 3/2`

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted September 18, 2013 at 10:59 PM (Answer #2)

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Solve `(4x-2)^2 - 5 = 11`

Add 5 to each side.

`(4x - 2)^2 = 16`

Take the square root of each side.

`4x - 2 =+- 4`

So this yields the 2 equations:

`4x - 2 = 4` and `4x - 2 = -4`

`4x - 2 = 4rArr 4x = 6rArr x = 3/2`

`4x - 2 = -4rArr 4x = -2rArr x = -1/2`

``So the answer is:

`x = 3/2, -1/2`

``

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atyourservice | Student, Grade 10 | (Level 3) Valedictorian

Posted March 16, 2014 at 2:06 AM (Answer #3)

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(4x - 2)^2 - 5 = 11

                 +5   +5

`(4x - 2)^2 = 16`

`sqrt((4x - 2)^2)= sqrt(16)`

`4x-2=+-4`

`4x-2=4`

`x=3/2`

`4x+2=-4`

`x=(-1)/2`

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