x^2+14x+49=40

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


Simplifying
x2 + 14x + 49 = 40

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

Solving
49 + 14x + x2 = 40

Solving for variable 'x'.

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

Combine like terms: 49 + -40 = 9
9 + 14x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
9 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 14x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 14x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 14x + x2 = 0 + -9
14x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
14x + x2 = -9

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 = -9 + 49

Reorder the terms:
49 + 14x + x2 = -9 + 49

Combine like terms: -9 + 49 = 40
49 + 14x + x2 = 40

Factor a perfect square on the left side:
(x + 7)(x + 7) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 7) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + 7 = 6.32455532

Simplifying
x + 7 = 6.32455532

Reorder the terms:
7 + x = 6.32455532

Solving
7 + x = 6.32455532

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 = 6.32455532 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.32455532 + -7
x = 6.32455532 + -7

Combine like terms: 6.32455532 + -7 = -0.67544468
x = -0.67544468

Simplifying
x = -0.67544468


Subproblem 2
x + 7 = -6.32455532

Simplifying
x + 7 = -6.32455532

Reorder the terms:
7 + x = -6.32455532

Solving
7 + x = -6.32455532

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 = -6.32455532 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.32455532 + -7
x = -6.32455532 + -7

Combine like terms: -6.32455532 + -7 = -13.32455532
x = -13.32455532

Simplifying
x = -13.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.67544468, -13.32455532}

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