x^2+x^2+14x+49=4x^2-40x-49

Solution for x^2+x^2+14x+49=4x^2-40x-49 equation:

Simplifying
x2 + x2 + 14x + 49 = 4x2 + -40x + -49

Reorder the terms:
49 + 14x + x2 + x2 = 4x2 + -40x + -49

Combine like terms: x2 + x2 = 2x2
49 + 14x + 2x2 = 4x2 + -40x + -49

Reorder the terms:
49 + 14x + 2x2 = -49 + -40x + 4x2

Solving
49 + 14x + 2x2 = -49 + -40x + 4x2

Solving for variable 'x'.

Reorder the terms:
49 + 49 + 14x + 40x + 2x2 + -4x2 = -49 + -40x + 4x2 + 49 + 40x + -4x2

Combine like terms: 49 + 49 = 98
98 + 14x + 40x + 2x2 + -4x2 = -49 + -40x + 4x2 + 49 + 40x + -4x2

Combine like terms: 14x + 40x = 54x
98 + 54x + 2x2 + -4x2 = -49 + -40x + 4x2 + 49 + 40x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
98 + 54x + -2x2 = -49 + -40x + 4x2 + 49 + 40x + -4x2

Reorder the terms:
98 + 54x + -2x2 = -49 + 49 + -40x + 40x + 4x2 + -4x2

Combine like terms: -49 + 49 = 0
98 + 54x + -2x2 = 0 + -40x + 40x + 4x2 + -4x2
98 + 54x + -2x2 = -40x + 40x + 4x2 + -4x2

Combine like terms: -40x + 40x = 0
98 + 54x + -2x2 = 0 + 4x2 + -4x2
98 + 54x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
98 + 54x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(49 + 27x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(49 + 27x + -1x2)' equal to zero and attempt to solve:

Simplifying
49 + 27x + -1x2 = 0

Solving
49 + 27x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-49 + -27x + x2 = 0

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -27x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + -27x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -27x + x2 = 0 + 49
-27x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
-27x + x2 = 49

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = 49 + 182.25

Reorder the terms:
182.25 + -27x + x2 = 49 + 182.25

Combine like terms: 49 + 182.25 = 231.25
182.25 + -27x + x2 = 231.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 231.25

Calculate the square root of the right side: 15.206906326

Break this problem into two subproblems by setting 
(x + -13.5) equal to 15.206906326 and -15.206906326.

Subproblem 1
x + -13.5 = 15.206906326

Simplifying
x + -13.5 = 15.206906326

Reorder the terms:
-13.5 + x = 15.206906326

Solving
-13.5 + x = 15.206906326

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = 15.206906326 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = 15.206906326 + 13.5
x = 15.206906326 + 13.5

Combine like terms: 15.206906326 + 13.5 = 28.706906326
x = 28.706906326

Simplifying
x = 28.706906326

Subproblem 2
x + -13.5 = -15.206906326

Simplifying
x + -13.5 = -15.206906326

Reorder the terms:
-13.5 + x = -15.206906326

Solving
-13.5 + x = -15.206906326

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = -15.206906326 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = -15.206906326 + 13.5
x = -15.206906326 + 13.5

Combine like terms: -15.206906326 + 13.5 = -1.706906326
x = -1.706906326

Simplifying
x = -1.706906326

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.706906326, -1.706906326}
Solution
x = {28.706906326, -1.706906326}