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Solve: `(a+3)^2 + (a-1)^2 = 26`  (a+3)^2 + (a-1)^2 = 26

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windowsisbett... | Student | Honors

Posted September 10, 2013 at 9:44 AM via web

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Solve: `(a+3)^2 + (a-1)^2 = 26`

 (a+3)^2 + (a-1)^2 = 26

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

Posted September 10, 2013 at 10:03 AM (Answer #1)

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To solve:   `(a+3)^2 + (a-1)^2 = 26`

First expand the brackets:

`therefore (a^2+3a +3a +9)+(a^2-a-a+1) -26 = 0`

Combine like terms:

`therefore 2a^2+4a-16 = 0`

Simplify by dividing by 2:

`therefore a^2+2a-8=0`

Now solve using the factors of the 1st term (`a times a` ) and the factors of the 3rd term which combine to render a middle term of 2a (`4 times -2` ) :

`therefore (a+4)(a-2)=0`

Now make each term =0

`therefore a+4=0`     and    `a-2=0`

`therefore a=-4`        and    `a=2`

Ans: To solve `(a+3)^2 + (a-1)^2 = 26`  a=-4 and a=2

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