x^2+7x=68

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Solution for x^2+7x=68 equation: 


Simplifying
x2 + 7x = 68

Reorder the terms:
7x + x2 = 68

Solving
7x + x2 = 68

Solving for variable 'x'.

Reorder the terms:
-68 + 7x + x2 = 68 + -68

Combine like terms: 68 + -68 = 0
-68 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 7x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + 7x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 7x + x2 = 0 + 68
7x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
7x + x2 = 68

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 68 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 68 + 12.25

Combine like terms: 68 + 12.25 = 80.25
12.25 + 7x + x2 = 80.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(x + 3.5) equal to 8.958236434 and -8.958236434.


Subproblem 1
x + 3.5 = 8.958236434

Simplifying
x + 3.5 = 8.958236434

Reorder the terms:
3.5 + x = 8.958236434

Solving
3.5 + x = 8.958236434

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 8.958236434 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 8.958236434 + -3.5
x = 8.958236434 + -3.5

Combine like terms: 8.958236434 + -3.5 = 5.458236434
x = 5.458236434

Simplifying
x = 5.458236434


Subproblem 2
x + 3.5 = -8.958236434

Simplifying
x + 3.5 = -8.958236434

Reorder the terms:
3.5 + x = -8.958236434

Solving
3.5 + x = -8.958236434

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -8.958236434 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -8.958236434 + -3.5
x = -8.958236434 + -3.5

Combine like terms: -8.958236434 + -3.5 = -12.458236434
x = -12.458236434

Simplifying
x = -12.458236434


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.458236434, -12.458236434}

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