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(x+3)2 = 49 (your original equation)
(x+3)2 = 72 (your equation showing 49 as the square of 7)
√(x+3)2) = √(72) (take the square root of both sides)
(x+3) = ±7 (evaluate the square root. Note there are 2 answers.)
x = ±7 - 3 (subtract 3 from both sides)
x = +4 or -10
_____
We could have written ±(x+3) = ±7. This would give the following:
+(x+3) = +7
-(x+3) = +7
+(x+3) = -7
-(x+3) = -7
The first on the list gives the same result as the last on the list, and the middle two give the same result. These two different results are adequately represented by using the ± sign on one side only, when taking the square root of both sides of the equation.
(x+3)2 = 72 (your equation showing 49 as the square of 7)
√(x+3)2) = √(72) (take the square root of both sides)
(x+3) = ±7 (evaluate the square root. Note there are 2 answers.)
x = ±7 - 3 (subtract 3 from both sides)
x = +4 or -10
_____
We could have written ±(x+3) = ±7. This would give the following:
+(x+3) = +7
-(x+3) = +7
+(x+3) = -7
-(x+3) = -7
The first on the list gives the same result as the last on the list, and the middle two give the same result. These two different results are adequately represented by using the ± sign on one side only, when taking the square root of both sides of the equation.
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