(x+9)*(x+12)=1

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Solution for (x+9)*(x+12)=1 equation:


Simplifying
(x + 9)(x + 12) = 1

Reorder the terms:
(9 + x)(x + 12) = 1

Reorder the terms:
(9 + x)(12 + x) = 1

Multiply (9 + x) * (12 + x)
(9(12 + x) + x(12 + x)) = 1
((12 * 9 + x * 9) + x(12 + x)) = 1
((108 + 9x) + x(12 + x)) = 1
(108 + 9x + (12 * x + x * x)) = 1
(108 + 9x + (12x + x2)) = 1

Combine like terms: 9x + 12x = 21x
(108 + 21x + x2) = 1

Solving
108 + 21x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
108 + -1 + 21x + x2 = 1 + -1

Combine like terms: 108 + -1 = 107
107 + 21x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
107 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-107' to each side of the equation.
107 + 21x + -107 + x2 = 0 + -107

Reorder the terms:
107 + -107 + 21x + x2 = 0 + -107

Combine like terms: 107 + -107 = 0
0 + 21x + x2 = 0 + -107
21x + x2 = 0 + -107

Combine like terms: 0 + -107 = -107
21x + x2 = -107

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -107 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -107 + 110.25

Combine like terms: -107 + 110.25 = 3.25
110.25 + 21x + x2 = 3.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 10.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

x + 10.5 = 1.802775638 Simplifying x + 10.5 = 1.802775638 Reorder the terms: 10.5 + x = 1.802775638 Solving 10.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 1.802775638 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 1.802775638 + -10.5 x = 1.802775638 + -10.5 Combine like terms: 1.802775638 + -10.5 = -8.697224362 x = -8.697224362 Simplifying x = -8.697224362

Subproblem 2

x + 10.5 = -1.802775638 Simplifying x + 10.5 = -1.802775638 Reorder the terms: 10.5 + x = -1.802775638 Solving 10.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -1.802775638 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -1.802775638 + -10.5 x = -1.802775638 + -10.5 Combine like terms: -1.802775638 + -10.5 = -12.302775638 x = -12.302775638 Simplifying x = -12.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-8.697224362, -12.302775638}

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