(x-5)(x-5)=49

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Solution for (x-5)(x-5)=49 equation: 


Simplifying
(x + -5)(x + -5) = 49

Reorder the terms:
(-5 + x)(x + -5) = 49

Reorder the terms:
(-5 + x)(-5 + x) = 49

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) = 49
((-5 * -5 + x * -5) + x(-5 + x)) = 49
((25 + -5x) + x(-5 + x)) = 49
(25 + -5x + (-5 * x + x * x)) = 49
(25 + -5x + (-5x + x2)) = 49

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) = 49

Solving
25 + -10x + x2 = 49

Solving for variable 'x'.

Reorder the terms:
25 + -49 + -10x + x2 = 49 + -49

Combine like terms: 25 + -49 = -24
-24 + -10x + x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-24 + -10x + x2 = 0

Factor a trinomial.
(-2 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-2, 12}

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