4(x+12)111x-25=0

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Solution for 4(x+12)111x-25=0 equation:


Simplifying
4(x + 12) * 111x + -25 = 0

Reorder the terms:
4(12 + x) * 111x + -25 = 0

Reorder the terms for easier multiplication:
4 * 111x(12 + x) + -25 = 0

Multiply 4 * 111
444x(12 + x) + -25 = 0
(12 * 444x + x * 444x) + -25 = 0
(5328x + 444x2) + -25 = 0

Reorder the terms:
-25 + 5328x + 444x2 = 0

Solving
-25 + 5328x + 444x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
444 the coefficient of the squared term: 

Divide each side by '444'.
-0.05630630631 + 12x + x2 = 0

Move the constant term to the right:

Add '0.05630630631' to each side of the equation.
-0.05630630631 + 12x + 0.05630630631 + x2 = 0 + 0.05630630631

Reorder the terms:
-0.05630630631 + 0.05630630631 + 12x + x2 = 0 + 0.05630630631

Combine like terms: -0.05630630631 + 0.05630630631 = 0.00000000000
0.00000000000 + 12x + x2 = 0 + 0.05630630631
12x + x2 = 0 + 0.05630630631

Combine like terms: 0 + 0.05630630631 = 0.05630630631
12x + x2 = 0.05630630631

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 = 0.05630630631 + 36

Reorder the terms:
36 + 12x + x2 = 0.05630630631 + 36

Combine like terms: 0.05630630631 + 36 = 36.05630630631
36 + 12x + x2 = 36.05630630631

Factor a perfect square on the left side:
(x + 6)(x + 6) = 36.05630630631

Calculate the square root of the right side: 6.004690359

Break this problem into two subproblems by setting 
(x + 6) equal to 6.004690359 and -6.004690359.

Subproblem 1

x + 6 = 6.004690359 Simplifying x + 6 = 6.004690359 Reorder the terms: 6 + x = 6.004690359 Solving 6 + x = 6.004690359 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 = 6.004690359 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.004690359 + -6 x = 6.004690359 + -6 Combine like terms: 6.004690359 + -6 = 0.004690359 x = 0.004690359 Simplifying x = 0.004690359

Subproblem 2

x + 6 = -6.004690359 Simplifying x + 6 = -6.004690359 Reorder the terms: 6 + x = -6.004690359 Solving 6 + x = -6.004690359 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 = -6.004690359 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.004690359 + -6 x = -6.004690359 + -6 Combine like terms: -6.004690359 + -6 = -12.004690359 x = -12.004690359 Simplifying x = -12.004690359

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.004690359, -12.004690359}

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