How do you solve $( x + 1 )^2 =25$ ?

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Answer 1 · 2016-05-08T18:31:31

Use the difference of squares identity to find:

$x=4$ or $x=-6$

The difference of squares identity can be written:

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

Use this with $a=(x+1)$ and $b=5$ as follows...

Subtract $25$ from both sides of the equation to find:

$0 = (x+1)^2-25$

$= (x+1)^2-5^2$

$=((x+1)-5)((x+1)+5)$

$=(x-4)(x+6)$

Hence $x=4$ or $x=-6$

How do you solve ( x + 1 )^2 =25( x + 1 )^2 =25?