x^2+7x+7x+49=10

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Solution for x^2+7x+7x+49=10 equation: 


Simplifying
x2 + 7x + 7x + 49 = 10

Reorder the terms:
49 + 7x + 7x + x2 = 10

Combine like terms: 7x + 7x = 14x
49 + 14x + x2 = 10

Solving
49 + 14x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
49 + -10 + 14x + x2 = 10 + -10

Combine like terms: 49 + -10 = 39
39 + 14x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
39 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 14x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + 14x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 14x + x2 = 0 + -39
14x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
14x + x2 = -39

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 = -39 + 49

Reorder the terms:
49 + 14x + x2 = -39 + 49

Combine like terms: -39 + 49 = 10
49 + 14x + x2 = 10

Factor a perfect square on the left side:
(x + 7)(x + 7) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 7) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 7 = 3.16227766

Simplifying
x + 7 = 3.16227766

Reorder the terms:
7 + x = 3.16227766

Solving
7 + x = 3.16227766

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 = 3.16227766 + -7

Combine like terms: 7 + -7 = 0
0 + x = 3.16227766 + -7
x = 3.16227766 + -7

Combine like terms: 3.16227766 + -7 = -3.83772234
x = -3.83772234

Simplifying
x = -3.83772234


Subproblem 2
x + 7 = -3.16227766

Simplifying
x + 7 = -3.16227766

Reorder the terms:
7 + x = -3.16227766

Solving
7 + x = -3.16227766

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 = -3.16227766 + -7

Combine like terms: 7 + -7 = 0
0 + x = -3.16227766 + -7
x = -3.16227766 + -7

Combine like terms: -3.16227766 + -7 = -10.16227766
x = -10.16227766

Simplifying
x = -10.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.83772234, -10.16227766}

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