(x-5)(x-5)-2x-4=0

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Solution for (x-5)(x-5)-2x-4=0 equation:


Simplifying
(x + -5)(x + -5) + -2x + -4 = 0

Reorder the terms:
(-5 + x)(x + -5) + -2x + -4 = 0

Reorder the terms:
(-5 + x)(-5 + x) + -2x + -4 = 0

Multiply (-5 + x) * (-5 + x)
(-5(-5 + x) + x(-5 + x)) + -2x + -4 = 0
((-5 * -5 + x * -5) + x(-5 + x)) + -2x + -4 = 0
((25 + -5x) + x(-5 + x)) + -2x + -4 = 0
(25 + -5x + (-5 * x + x * x)) + -2x + -4 = 0
(25 + -5x + (-5x + x2)) + -2x + -4 = 0

Combine like terms: -5x + -5x = -10x
(25 + -10x + x2) + -2x + -4 = 0

Reorder the terms:
25 + -4 + -10x + -2x + x2 = 0

Combine like terms: 25 + -4 = 21
21 + -10x + -2x + x2 = 0

Combine like terms: -10x + -2x = -12x
21 + -12x + x2 = 0

Solving
21 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -12x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -12x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -12x + x2 = 0 + -21
-12x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-12x + x2 = -21

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -21 + 36

Reorder the terms:
36 + -12x + x2 = -21 + 36

Combine like terms: -21 + 36 = 15
36 + -12x + x2 = 15

Factor a perfect square on the left side:
(x + -6)(x + -6) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -6) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + -6 = 3.872983346 Simplifying x + -6 = 3.872983346 Reorder the terms: -6 + x = 3.872983346 Solving -6 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.872983346 + 6 x = 3.872983346 + 6 Combine like terms: 3.872983346 + 6 = 9.872983346 x = 9.872983346 Simplifying x = 9.872983346

Subproblem 2

x + -6 = -3.872983346 Simplifying x + -6 = -3.872983346 Reorder the terms: -6 + x = -3.872983346 Solving -6 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.872983346 + 6 x = -3.872983346 + 6 Combine like terms: -3.872983346 + 6 = 2.127016654 x = 2.127016654 Simplifying x = 2.127016654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.872983346, 2.127016654}

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