12-4x-x^2=36-16x^2+16

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Solution for 12-4x-x^2=36-16x^2+16 equation:


Simplifying
12 + -4x + -1x2 = 36 + -16x2 + 16

Reorder the terms:
12 + -4x + -1x2 = 36 + 16 + -16x2

Combine like terms: 36 + 16 = 52
12 + -4x + -1x2 = 52 + -16x2

Solving
12 + -4x + -1x2 = 52 + -16x2

Solving for variable 'x'.

Reorder the terms:
12 + -52 + -4x + -1x2 + 16x2 = 52 + -16x2 + -52 + 16x2

Combine like terms: 12 + -52 = -40
-40 + -4x + -1x2 + 16x2 = 52 + -16x2 + -52 + 16x2

Combine like terms: -1x2 + 16x2 = 15x2
-40 + -4x + 15x2 = 52 + -16x2 + -52 + 16x2

Reorder the terms:
-40 + -4x + 15x2 = 52 + -52 + -16x2 + 16x2

Combine like terms: 52 + -52 = 0
-40 + -4x + 15x2 = 0 + -16x2 + 16x2
-40 + -4x + 15x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-40 + -4x + 15x2 = 0

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

Divide each side by '15'.
-2.666666667 + -0.2666666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -0.2666666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -0.2666666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -0.2666666667x + x2 = 0 + 2.666666667
-0.2666666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-0.2666666667x + x2 = 2.666666667

The x term is -0.2666666667x.  Take half its coefficient (-0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
-0.2666666667x + 0.01777777780 + x2 = 2.666666667 + 0.01777777780

Reorder the terms:
0.01777777780 + -0.2666666667x + x2 = 2.666666667 + 0.01777777780

Combine like terms: 2.666666667 + 0.01777777780 = 2.6844444448
0.01777777780 + -0.2666666667x + x2 = 2.6844444448

Factor a perfect square on the left side:
(x + -0.1333333334)(x + -0.1333333334) = 2.6844444448

Calculate the square root of the right side: 1.63842743

Break this problem into two subproblems by setting 
(x + -0.1333333334) equal to 1.63842743 and -1.63842743.

Subproblem 1

x + -0.1333333334 = 1.63842743 Simplifying x + -0.1333333334 = 1.63842743 Reorder the terms: -0.1333333334 + x = 1.63842743 Solving -0.1333333334 + x = 1.63842743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = 1.63842743 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = 1.63842743 + 0.1333333334 x = 1.63842743 + 0.1333333334 Combine like terms: 1.63842743 + 0.1333333334 = 1.7717607634 x = 1.7717607634 Simplifying x = 1.7717607634

Subproblem 2

x + -0.1333333334 = -1.63842743 Simplifying x + -0.1333333334 = -1.63842743 Reorder the terms: -0.1333333334 + x = -1.63842743 Solving -0.1333333334 + x = -1.63842743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = -1.63842743 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = -1.63842743 + 0.1333333334 x = -1.63842743 + 0.1333333334 Combine like terms: -1.63842743 + 0.1333333334 = -1.5050940966 x = -1.5050940966 Simplifying x = -1.5050940966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7717607634, -1.5050940966}

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