x^2+0.85x-68=0

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Solution for x^2+0.85x-68=0 equation: 


Simplifying
x2 + 0.85x + -68 = 0

Reorder the terms:
-68 + 0.85x + x2 = 0

Solving
-68 + 0.85x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 0.85x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + 0.85x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 0.85x + x2 = 0 + 68
0.85x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
0.85x + x2 = 68

The x term is 0.85x.  Take half its coefficient (0.425).
Square it (0.180625) and add it to both sides.

Add '0.180625' to each side of the equation.
0.85x + 0.180625 + x2 = 68 + 0.180625

Reorder the terms:
0.180625 + 0.85x + x2 = 68 + 0.180625

Combine like terms: 68 + 0.180625 = 68.180625
0.180625 + 0.85x + x2 = 68.180625

Factor a perfect square on the left side:
(x + 0.425)(x + 0.425) = 68.180625

Calculate the square root of the right side: 8.257155987

Break this problem into two subproblems by setting 
(x + 0.425) equal to 8.257155987 and -8.257155987.


Subproblem 1
x + 0.425 = 8.257155987

Simplifying
x + 0.425 = 8.257155987

Reorder the terms:
0.425 + x = 8.257155987

Solving
0.425 + x = 8.257155987

Solving for variable 'x'.

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

Add '-0.425' to each side of the equation.
0.425 + -0.425 + x = 8.257155987 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = 8.257155987 + -0.425
x = 8.257155987 + -0.425

Combine like terms: 8.257155987 + -0.425 = 7.832155987
x = 7.832155987

Simplifying
x = 7.832155987


Subproblem 2
x + 0.425 = -8.257155987

Simplifying
x + 0.425 = -8.257155987

Reorder the terms:
0.425 + x = -8.257155987

Solving
0.425 + x = -8.257155987

Solving for variable 'x'.

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

Add '-0.425' to each side of the equation.
0.425 + -0.425 + x = -8.257155987 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = -8.257155987 + -0.425
x = -8.257155987 + -0.425

Combine like terms: -8.257155987 + -0.425 = -8.682155987
x = -8.682155987

Simplifying
x = -8.682155987


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.832155987, -8.682155987}

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