(x+12)(x+10)=2

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Solution for (x+12)(x+10)=2 equation:


Simplifying
(x + 12)(x + 10) = 2

Reorder the terms:
(12 + x)(x + 10) = 2

Reorder the terms:
(12 + x)(10 + x) = 2

Multiply (12 + x) * (10 + x)
(12(10 + x) + x(10 + x)) = 2
((10 * 12 + x * 12) + x(10 + x)) = 2
((120 + 12x) + x(10 + x)) = 2
(120 + 12x + (10 * x + x * x)) = 2
(120 + 12x + (10x + x2)) = 2

Combine like terms: 12x + 10x = 22x
(120 + 22x + x2) = 2

Solving
120 + 22x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
120 + -2 + 22x + x2 = 2 + -2

Combine like terms: 120 + -2 = 118
118 + 22x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
118 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-118' to each side of the equation.
118 + 22x + -118 + x2 = 0 + -118

Reorder the terms:
118 + -118 + 22x + x2 = 0 + -118

Combine like terms: 118 + -118 = 0
0 + 22x + x2 = 0 + -118
22x + x2 = 0 + -118

Combine like terms: 0 + -118 = -118
22x + x2 = -118

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -118 + 121

Reorder the terms:
121 + 22x + x2 = -118 + 121

Combine like terms: -118 + 121 = 3
121 + 22x + x2 = 3

Factor a perfect square on the left side:
(x + 11)(x + 11) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 11) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 11 = 1.732050808 Simplifying x + 11 = 1.732050808 Reorder the terms: 11 + x = 1.732050808 Solving 11 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 1.732050808 + -11 Combine like terms: 11 + -11 = 0 0 + x = 1.732050808 + -11 x = 1.732050808 + -11 Combine like terms: 1.732050808 + -11 = -9.267949192 x = -9.267949192 Simplifying x = -9.267949192

Subproblem 2

x + 11 = -1.732050808 Simplifying x + 11 = -1.732050808 Reorder the terms: 11 + x = -1.732050808 Solving 11 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -1.732050808 + -11 Combine like terms: 11 + -11 = 0 0 + x = -1.732050808 + -11 x = -1.732050808 + -11 Combine like terms: -1.732050808 + -11 = -12.732050808 x = -12.732050808 Simplifying x = -12.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-9.267949192, -12.732050808}

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