2x^2+3x-4+7x+8=-4x^2-12x+17

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Solution for 2x^2+3x-4+7x+8=-4x^2-12x+17 equation: 


Simplifying
2x2 + 3x + -4 + 7x + 8 = -4x2 + -12x + 17

Reorder the terms:
-4 + 8 + 3x + 7x + 2x2 = -4x2 + -12x + 17

Combine like terms: -4 + 8 = 4
4 + 3x + 7x + 2x2 = -4x2 + -12x + 17

Combine like terms: 3x + 7x = 10x
4 + 10x + 2x2 = -4x2 + -12x + 17

Reorder the terms:
4 + 10x + 2x2 = 17 + -12x + -4x2

Solving
4 + 10x + 2x2 = 17 + -12x + -4x2

Solving for variable 'x'.

Reorder the terms:
4 + -17 + 10x + 12x + 2x2 + 4x2 = 17 + -12x + -4x2 + -17 + 12x + 4x2

Combine like terms: 4 + -17 = -13
-13 + 10x + 12x + 2x2 + 4x2 = 17 + -12x + -4x2 + -17 + 12x + 4x2

Combine like terms: 10x + 12x = 22x
-13 + 22x + 2x2 + 4x2 = 17 + -12x + -4x2 + -17 + 12x + 4x2

Combine like terms: 2x2 + 4x2 = 6x2
-13 + 22x + 6x2 = 17 + -12x + -4x2 + -17 + 12x + 4x2

Reorder the terms:
-13 + 22x + 6x2 = 17 + -17 + -12x + 12x + -4x2 + 4x2

Combine like terms: 17 + -17 = 0
-13 + 22x + 6x2 = 0 + -12x + 12x + -4x2 + 4x2
-13 + 22x + 6x2 = -12x + 12x + -4x2 + 4x2

Combine like terms: -12x + 12x = 0
-13 + 22x + 6x2 = 0 + -4x2 + 4x2
-13 + 22x + 6x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-13 + 22x + 6x2 = 0

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

Divide each side by '6'.
-2.166666667 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + 3.666666667x + 2.166666667 + x2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + 3.666666667x + x2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + 3.666666667x + x2 = 0 + 2.166666667
3.666666667x + x2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
3.666666667x + x2 = 2.166666667

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = 2.166666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 2.166666667 + 3.361111114

Combine like terms: 2.166666667 + 3.361111114 = 5.527777781
3.361111114 + 3.666666667x + x2 = 5.527777781

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 5.527777781

Calculate the square root of the right side: 2.351122664

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 2.351122664 and -2.351122664.


Subproblem 1
x + 1.833333334 = 2.351122664

Simplifying
x + 1.833333334 = 2.351122664

Reorder the terms:
1.833333334 + x = 2.351122664

Solving
1.833333334 + x = 2.351122664

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = 2.351122664 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 2.351122664 + -1.833333334
x = 2.351122664 + -1.833333334

Combine like terms: 2.351122664 + -1.833333334 = 0.51778933
x = 0.51778933

Simplifying
x = 0.51778933


Subproblem 2
x + 1.833333334 = -2.351122664

Simplifying
x + 1.833333334 = -2.351122664

Reorder the terms:
1.833333334 + x = -2.351122664

Solving
1.833333334 + x = -2.351122664

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = -2.351122664 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -2.351122664 + -1.833333334
x = -2.351122664 + -1.833333334

Combine like terms: -2.351122664 + -1.833333334 = -4.184455998
x = -4.184455998

Simplifying
x = -4.184455998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.51778933, -4.184455998}

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