(x-5)(x-5)+4x=52

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Solution for (x-5)(x-5)+4x=52 equation: 


Simplifying
(x + -5)(x + -5) + 4x = 52

Reorder the terms:
(-5 + x)(x + -5) + 4x = 52

Reorder the terms:
(-5 + x)(-5 + x) + 4x = 52

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + 4x = 52
((-5 * -5 + x * -5) + x(-5 + x)) + 4x = 52
((25 + -5x) + x(-5 + x)) + 4x = 52
(25 + -5x + (-5 * x + x * x)) + 4x = 52
(25 + -5x + (-5x + x2)) + 4x = 52

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + 4x = 52

Reorder the terms:
25 + -10x + 4x + x2 = 52

Combine like terms: -10x + 4x = -6x
25 + -6x + x2 = 52

Solving
25 + -6x + x2 = 52

Solving for variable 'x'.

Reorder the terms:
25 + -52 + -6x + x2 = 52 + -52

Combine like terms: 25 + -52 = -27
-27 + -6x + x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-27 + -6x + x2 = 0

Factor a trinomial.
(-3 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-3, 9}

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