13-3(x^2+14x+49)=0

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Solution for 13-3(x^2+14x+49)=0 equation: 


Simplifying
13 + -3(x2 + 14x + 49) = 0

Reorder the terms:
13 + -3(49 + 14x + x2) = 0
13 + (49 * -3 + 14x * -3 + x2 * -3) = 0
13 + (-147 + -42x + -3x2) = 0

Combine like terms: 13 + -147 = -134
-134 + -42x + -3x2 = 0

Solving
-134 + -42x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(134 + 42x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(134 + 42x + 3x2)' equal to zero and attempt to solve:

Simplifying
134 + 42x + 3x2 = 0

Solving
134 + 42x + 3x2 = 0

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

Divide each side by '3'.
44.66666667 + 14x + x2 = 0

Move the constant term to the right:

Add '-44.66666667' to each side of the equation.
44.66666667 + 14x + -44.66666667 + x2 = 0 + -44.66666667

Reorder the terms:
44.66666667 + -44.66666667 + 14x + x2 = 0 + -44.66666667

Combine like terms: 44.66666667 + -44.66666667 = 0.00000000
0.00000000 + 14x + x2 = 0 + -44.66666667
14x + x2 = 0 + -44.66666667

Combine like terms: 0 + -44.66666667 = -44.66666667
14x + x2 = -44.66666667

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -44.66666667 + 49

Reorder the terms:
49 + 14x + x2 = -44.66666667 + 49

Combine like terms: -44.66666667 + 49 = 4.33333333
49 + 14x + x2 = 4.33333333

Factor a perfect square on the left side:
(x + 7)(x + 7) = 4.33333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(x + 7) equal to 2.081665999 and -2.081665999.


Subproblem 1
x + 7 = 2.081665999

Simplifying
x + 7 = 2.081665999

Reorder the terms:
7 + x = 2.081665999

Solving
7 + x = 2.081665999

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 2.081665999 + -7

Combine like terms: 7 + -7 = 0
0 + x = 2.081665999 + -7
x = 2.081665999 + -7

Combine like terms: 2.081665999 + -7 = -4.918334001
x = -4.918334001

Simplifying
x = -4.918334001


Subproblem 2
x + 7 = -2.081665999

Simplifying
x + 7 = -2.081665999

Reorder the terms:
7 + x = -2.081665999

Solving
7 + x = -2.081665999

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -2.081665999 + -7

Combine like terms: 7 + -7 = 0
0 + x = -2.081665999 + -7
x = -2.081665999 + -7

Combine like terms: -2.081665999 + -7 = -9.081665999
x = -9.081665999

Simplifying
x = -9.081665999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.918334001, -9.081665999}
Solution
x = {-4.918334001, -9.081665999}

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