x^2+34x=4x^2+165x+85

Solution for x^2+34x=4x^2+165x+85 equation:

Simplifying
x2 + 34x = 4x2 + 165x + 85

Reorder the terms:
34x + x2 = 4x2 + 165x + 85

Reorder the terms:
34x + x2 = 85 + 165x + 4x2

Solving
34x + x2 = 85 + 165x + 4x2

Solving for variable 'x'.

Reorder the terms:
-85 + 34x + -165x + x2 + -4x2 = 85 + 165x + 4x2 + -85 + -165x + -4x2

Combine like terms: 34x + -165x = -131x
-85 + -131x + x2 + -4x2 = 85 + 165x + 4x2 + -85 + -165x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-85 + -131x + -3x2 = 85 + 165x + 4x2 + -85 + -165x + -4x2

Reorder the terms:
-85 + -131x + -3x2 = 85 + -85 + 165x + -165x + 4x2 + -4x2

Combine like terms: 85 + -85 = 0
-85 + -131x + -3x2 = 0 + 165x + -165x + 4x2 + -4x2
-85 + -131x + -3x2 = 165x + -165x + 4x2 + -4x2

Combine like terms: 165x + -165x = 0
-85 + -131x + -3x2 = 0 + 4x2 + -4x2
-85 + -131x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-85 + -131x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(85 + 131x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(85 + 131x + 3x2)' equal to zero and attempt to solve:

Simplifying
85 + 131x + 3x2 = 0

Solving
85 + 131x + 3x2 = 0

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

Divide each side by '3'.
28.33333333 + 43.66666667x + x2 = 0

Move the constant term to the right:

Add '-28.33333333' to each side of the equation.
28.33333333 + 43.66666667x + -28.33333333 + x2 = 0 + -28.33333333

Reorder the terms:
28.33333333 + -28.33333333 + 43.66666667x + x2 = 0 + -28.33333333

Combine like terms: 28.33333333 + -28.33333333 = 0.00000000
0.00000000 + 43.66666667x + x2 = 0 + -28.33333333
43.66666667x + x2 = 0 + -28.33333333

Combine like terms: 0 + -28.33333333 = -28.33333333
43.66666667x + x2 = -28.33333333

The x term is 43.66666667x.  Take half its coefficient (21.83333334).
Square it (476.6944447) and add it to both sides.

Add '476.6944447' to each side of the equation.
43.66666667x + 476.6944447 + x2 = -28.33333333 + 476.6944447

Reorder the terms:
476.6944447 + 43.66666667x + x2 = -28.33333333 + 476.6944447

Combine like terms: -28.33333333 + 476.6944447 = 448.36111137
476.6944447 + 43.66666667x + x2 = 448.36111137

Factor a perfect square on the left side:
(x + 21.83333334)(x + 21.83333334) = 448.36111137

Calculate the square root of the right side: 21.174539225

Break this problem into two subproblems by setting 
(x + 21.83333334) equal to 21.174539225 and -21.174539225.

Subproblem 1
x + 21.83333334 = 21.174539225

Simplifying
x + 21.83333334 = 21.174539225

Reorder the terms:
21.83333334 + x = 21.174539225

Solving
21.83333334 + x = 21.174539225

Solving for variable 'x'.

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

Add '-21.83333334' to each side of the equation.
21.83333334 + -21.83333334 + x = 21.174539225 + -21.83333334

Combine like terms: 21.83333334 + -21.83333334 = 0.00000000
0.00000000 + x = 21.174539225 + -21.83333334
x = 21.174539225 + -21.83333334

Combine like terms: 21.174539225 + -21.83333334 = -0.658794115
x = -0.658794115

Simplifying
x = -0.658794115

Subproblem 2
x + 21.83333334 = -21.174539225

Simplifying
x + 21.83333334 = -21.174539225

Reorder the terms:
21.83333334 + x = -21.174539225

Solving
21.83333334 + x = -21.174539225

Solving for variable 'x'.

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

Add '-21.83333334' to each side of the equation.
21.83333334 + -21.83333334 + x = -21.174539225 + -21.83333334

Combine like terms: 21.83333334 + -21.83333334 = 0.00000000
0.00000000 + x = -21.174539225 + -21.83333334
x = -21.174539225 + -21.83333334

Combine like terms: -21.174539225 + -21.83333334 = -43.007872565
x = -43.007872565

Simplifying
x = -43.007872565

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.658794115, -43.007872565}
Solution
x = {-0.658794115, -43.007872565}