x^2+7x-85=0

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Solution for x^2+7x-85=0 equation: 


Simplifying
x2 + 7x + -85 = 0

Reorder the terms:
-85 + 7x + x2 = 0

Solving
-85 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 7x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + 7x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 7x + x2 = 0 + 85
7x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
7x + x2 = 85

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 = 85 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 85 + 12.25

Combine like terms: 85 + 12.25 = 97.25
12.25 + 7x + x2 = 97.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 97.25

Calculate the square root of the right side: 9.861541462

Break this problem into two subproblems by setting 
(x + 3.5) equal to 9.861541462 and -9.861541462.


Subproblem 1
x + 3.5 = 9.861541462

Simplifying
x + 3.5 = 9.861541462

Reorder the terms:
3.5 + x = 9.861541462

Solving
3.5 + x = 9.861541462

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 = 9.861541462 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 9.861541462 + -3.5
x = 9.861541462 + -3.5

Combine like terms: 9.861541462 + -3.5 = 6.361541462
x = 6.361541462

Simplifying
x = 6.361541462


Subproblem 2
x + 3.5 = -9.861541462

Simplifying
x + 3.5 = -9.861541462

Reorder the terms:
3.5 + x = -9.861541462

Solving
3.5 + x = -9.861541462

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 = -9.861541462 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -9.861541462 + -3.5
x = -9.861541462 + -3.5

Combine like terms: -9.861541462 + -3.5 = -13.361541462
x = -13.361541462

Simplifying
x = -13.361541462


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.361541462, -13.361541462}

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