11x^2+9-12x-8x^2-13x=

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Solution for 11x^2+9-12x-8x^2-13x= equation:


Simplifying
11x2 + 9 + -12x + -8x2 + -13x = 0

Reorder the terms:
9 + -12x + -13x + 11x2 + -8x2 = 0

Combine like terms: -12x + -13x = -25x
9 + -25x + 11x2 + -8x2 = 0

Combine like terms: 11x2 + -8x2 = 3x2
9 + -25x + 3x2 = 0

Solving
9 + -25x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
3 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -8.333333333x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -8.333333333x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8.333333333x + x2 = 0 + -3
-8.333333333x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8.333333333x + x2 = -3

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -3 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -3 + 17.36111111

Combine like terms: -3 + 17.36111111 = 14.36111111
17.36111111 + -8.333333333x + x2 = 14.36111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 14.36111111

Calculate the square root of the right side: 3.789605667

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 3.789605667 and -3.789605667.

Subproblem 1

x + -4.166666667 = 3.789605667 Simplifying x + -4.166666667 = 3.789605667 Reorder the terms: -4.166666667 + x = 3.789605667 Solving -4.166666667 + x = 3.789605667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 3.789605667 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 3.789605667 + 4.166666667 x = 3.789605667 + 4.166666667 Combine like terms: 3.789605667 + 4.166666667 = 7.956272334 x = 7.956272334 Simplifying x = 7.956272334

Subproblem 2

x + -4.166666667 = -3.789605667 Simplifying x + -4.166666667 = -3.789605667 Reorder the terms: -4.166666667 + x = -3.789605667 Solving -4.166666667 + x = -3.789605667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -3.789605667 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -3.789605667 + 4.166666667 x = -3.789605667 + 4.166666667 Combine like terms: -3.789605667 + 4.166666667 = 0.377061 x = 0.377061 Simplifying x = 0.377061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.956272334, 0.377061}

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