2x^2+12x=9

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Solution for 2x^2+12x=9 equation:


Simplifying
2x2 + 12x = 9

Reorder the terms:
12x + 2x2 = 9

Solving
12x + 2x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 12x + 2x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 12x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + 6x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 6x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 6x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 6x + x2 = 0 + 4.5
6x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
6x + x2 = 4.5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 4.5 + 9

Reorder the terms:
9 + 6x + x2 = 4.5 + 9

Combine like terms: 4.5 + 9 = 13.5
9 + 6x + x2 = 13.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(x + 3) equal to 3.674234614 and -3.674234614.

Subproblem 1

x + 3 = 3.674234614 Simplifying x + 3 = 3.674234614 Reorder the terms: 3 + x = 3.674234614 Solving 3 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.674234614 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.674234614 + -3 x = 3.674234614 + -3 Combine like terms: 3.674234614 + -3 = 0.674234614 x = 0.674234614 Simplifying x = 0.674234614

Subproblem 2

x + 3 = -3.674234614 Simplifying x + 3 = -3.674234614 Reorder the terms: 3 + x = -3.674234614 Solving 3 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.674234614 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.674234614 + -3 x = -3.674234614 + -3 Combine like terms: -3.674234614 + -3 = -6.674234614 x = -6.674234614 Simplifying x = -6.674234614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.674234614, -6.674234614}

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