(14-2x)(10-2x)=88

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Solution for (14-2x)(10-2x)=88 equation: 


Simplifying
(14 + -2x)(10 + -2x) = 88

Multiply (14 + -2x) * (10 + -2x)
(14(10 + -2x) + -2x * (10 + -2x)) = 88
((10 * 14 + -2x * 14) + -2x * (10 + -2x)) = 88
((140 + -28x) + -2x * (10 + -2x)) = 88
(140 + -28x + (10 * -2x + -2x * -2x)) = 88
(140 + -28x + (-20x + 4x2)) = 88

Combine like terms: -28x + -20x = -48x
(140 + -48x + 4x2) = 88

Solving
140 + -48x + 4x2 = 88

Solving for variable 'x'.

Reorder the terms:
140 + -88 + -48x + 4x2 = 88 + -88

Combine like terms: 140 + -88 = 52
52 + -48x + 4x2 = 88 + -88

Combine like terms: 88 + -88 = 0
52 + -48x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(13 + -12x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(13 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
13 + -12x + x2 = 0

Solving
13 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -12x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -12x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -12x + x2 = 0 + -13
-12x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-12x + x2 = -13

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 = -13 + 36

Reorder the terms:
36 + -12x + x2 = -13 + 36

Combine like terms: -13 + 36 = 23
36 + -12x + x2 = 23

Factor a perfect square on the left side:
(x + -6)(x + -6) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + -6) equal to 4.795831523 and -4.795831523.


Subproblem 1
x + -6 = 4.795831523

Simplifying
x + -6 = 4.795831523

Reorder the terms:
-6 + x = 4.795831523

Solving
-6 + x = 4.795831523

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 = 4.795831523 + 6

Combine like terms: -6 + 6 = 0
0 + x = 4.795831523 + 6
x = 4.795831523 + 6

Combine like terms: 4.795831523 + 6 = 10.795831523
x = 10.795831523

Simplifying
x = 10.795831523


Subproblem 2
x + -6 = -4.795831523

Simplifying
x + -6 = -4.795831523

Reorder the terms:
-6 + x = -4.795831523

Solving
-6 + x = -4.795831523

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 = -4.795831523 + 6

Combine like terms: -6 + 6 = 0
0 + x = -4.795831523 + 6
x = -4.795831523 + 6

Combine like terms: -4.795831523 + 6 = 1.204168477
x = 1.204168477

Simplifying
x = 1.204168477


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.795831523, 1.204168477}
Solution
x = {10.795831523, 1.204168477}

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