(-15x^2-11x+23)-[(-7x^2-11x+7)-(11x^2-13x-5)]=

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Solution for (-15x^2-11x+23)-[(-7x^2-11x+7)-(11x^2-13x-5)]= equation: 


Simplifying
(-15x2 + -11x + 23) + -1[(-7x2 + -11x + 7) + -1(11x2 + -13x + -5)] = 0

Reorder the terms:
(23 + -11x + -15x2) + -1[(-7x2 + -11x + 7) + -1(11x2 + -13x + -5)] = 0

Remove parenthesis around (23 + -11x + -15x2)
23 + -11x + -15x2 + -1[(-7x2 + -11x + 7) + -1(11x2 + -13x + -5)] = 0

Reorder the terms:
23 + -11x + -15x2 + -1[(7 + -11x + -7x2) + -1(11x2 + -13x + -5)] = 0

Remove parenthesis around (7 + -11x + -7x2)
23 + -11x + -15x2 + -1[7 + -11x + -7x2 + -1(11x2 + -13x + -5)] = 0

Reorder the terms:
23 + -11x + -15x2 + -1[7 + -11x + -7x2 + -1(-5 + -13x + 11x2)] = 0
23 + -11x + -15x2 + -1[7 + -11x + -7x2 + (-5 * -1 + -13x * -1 + 11x2 * -1)] = 0
23 + -11x + -15x2 + -1[7 + -11x + -7x2 + (5 + 13x + -11x2)] = 0

Reorder the terms:
23 + -11x + -15x2 + -1[7 + 5 + -11x + 13x + -7x2 + -11x2] = 0

Combine like terms: 7 + 5 = 12
23 + -11x + -15x2 + -1[12 + -11x + 13x + -7x2 + -11x2] = 0

Combine like terms: -11x + 13x = 2x
23 + -11x + -15x2 + -1[12 + 2x + -7x2 + -11x2] = 0

Combine like terms: -7x2 + -11x2 = -18x2
23 + -11x + -15x2 + -1[12 + 2x + -18x2] = 0
23 + -11x + -15x2 + [12 * -1 + 2x * -1 + -18x2 * -1] = 0
23 + -11x + -15x2 + [-12 + -2x + 18x2] = 0

Reorder the terms:
23 + -12 + -11x + -2x + -15x2 + 18x2 = 0

Combine like terms: 23 + -12 = 11
11 + -11x + -2x + -15x2 + 18x2 = 0

Combine like terms: -11x + -2x = -13x
11 + -13x + -15x2 + 18x2 = 0

Combine like terms: -15x2 + 18x2 = 3x2
11 + -13x + 3x2 = 0

Solving
11 + -13x + 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'.
3.666666667 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -4.333333333x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -4.333333333x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -4.333333333x + x2 = 0 + -3.666666667
-4.333333333x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-4.333333333x + x2 = -3.666666667

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -3.666666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -3.666666667 + 4.694444446

Combine like terms: -3.666666667 + 4.694444446 = 1.027777779
4.694444446 + -4.333333333x + x2 = 1.027777779

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 1.027777779

Calculate the square root of the right side: 1.013793756

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 1.013793756 and -1.013793756.


Subproblem 1
x + -2.166666667 = 1.013793756

Simplifying
x + -2.166666667 = 1.013793756

Reorder the terms:
-2.166666667 + x = 1.013793756

Solving
-2.166666667 + x = 1.013793756

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 1.013793756 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 1.013793756 + 2.166666667
x = 1.013793756 + 2.166666667

Combine like terms: 1.013793756 + 2.166666667 = 3.180460423
x = 3.180460423

Simplifying
x = 3.180460423


Subproblem 2
x + -2.166666667 = -1.013793756

Simplifying
x + -2.166666667 = -1.013793756

Reorder the terms:
-2.166666667 + x = -1.013793756

Solving
-2.166666667 + x = -1.013793756

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -1.013793756 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -1.013793756 + 2.166666667
x = -1.013793756 + 2.166666667

Combine like terms: -1.013793756 + 2.166666667 = 1.152872911
x = 1.152872911

Simplifying
x = 1.152872911


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.180460423, 1.152872911}

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