x^2+12x=3.69

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Solution for x^2+12x=3.69 equation:


Simplifying
x2 + 12x = 3.69

Reorder the terms:
12x + x2 = 3.69

Solving
12x + x2 = 3.69

Solving for variable 'x'.

Reorder the terms:
-3.69 + 12x + x2 = 3.69 + -3.69

Combine like terms: 3.69 + -3.69 = 0.00
-3.69 + 12x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '3.69' to each side of the equation.
-3.69 + 12x + 3.69 + x2 = 0.00 + 3.69

Reorder the terms:
-3.69 + 3.69 + 12x + x2 = 0.00 + 3.69

Combine like terms: -3.69 + 3.69 = 0.00
0.00 + 12x + x2 = 0.00 + 3.69
12x + x2 = 0.00 + 3.69

Combine like terms: 0.00 + 3.69 = 3.69
12x + x2 = 3.69

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 = 3.69 + 36

Reorder the terms:
36 + 12x + x2 = 3.69 + 36

Combine like terms: 3.69 + 36 = 39.69
36 + 12x + x2 = 39.69

Factor a perfect square on the left side:
(x + 6)(x + 6) = 39.69

Calculate the square root of the right side: 6.3

Break this problem into two subproblems by setting 
(x + 6) equal to 6.3 and -6.3.

Subproblem 1

x + 6 = 6.3 Simplifying x + 6 = 6.3 Reorder the terms: 6 + x = 6.3 Solving 6 + x = 6.3 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 = 6.3 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.3 + -6 x = 6.3 + -6 Combine like terms: 6.3 + -6 = 0.3 x = 0.3 Simplifying x = 0.3

Subproblem 2

x + 6 = -6.3 Simplifying x + 6 = -6.3 Reorder the terms: 6 + x = -6.3 Solving 6 + x = -6.3 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 = -6.3 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.3 + -6 x = -6.3 + -6 Combine like terms: -6.3 + -6 = -12.3 x = -12.3 Simplifying x = -12.3

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3, -12.3}

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