x^2+0.85x-5.593=0

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Solution for x^2+0.85x-5.593=0 equation: 


Simplifying
x2 + 0.85x + -5.593 = 0

Reorder the terms:
-5.593 + 0.85x + x2 = 0

Solving
-5.593 + 0.85x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5.593' to each side of the equation.
-5.593 + 0.85x + 5.593 + x2 = 0 + 5.593

Reorder the terms:
-5.593 + 5.593 + 0.85x + x2 = 0 + 5.593

Combine like terms: -5.593 + 5.593 = 0.000
0.000 + 0.85x + x2 = 0 + 5.593
0.85x + x2 = 0 + 5.593

Combine like terms: 0 + 5.593 = 5.593
0.85x + x2 = 5.593

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 = 5.593 + 0.180625

Reorder the terms:
0.180625 + 0.85x + x2 = 5.593 + 0.180625

Combine like terms: 5.593 + 0.180625 = 5.773625
0.180625 + 0.85x + x2 = 5.773625

Factor a perfect square on the left side:
(x + 0.425)(x + 0.425) = 5.773625

Calculate the square root of the right side: 2.402836865

Break this problem into two subproblems by setting 
(x + 0.425) equal to 2.402836865 and -2.402836865.


Subproblem 1
x + 0.425 = 2.402836865

Simplifying
x + 0.425 = 2.402836865

Reorder the terms:
0.425 + x = 2.402836865

Solving
0.425 + x = 2.402836865

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 = 2.402836865 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = 2.402836865 + -0.425
x = 2.402836865 + -0.425

Combine like terms: 2.402836865 + -0.425 = 1.977836865
x = 1.977836865

Simplifying
x = 1.977836865


Subproblem 2
x + 0.425 = -2.402836865

Simplifying
x + 0.425 = -2.402836865

Reorder the terms:
0.425 + x = -2.402836865

Solving
0.425 + x = -2.402836865

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 = -2.402836865 + -0.425

Combine like terms: 0.425 + -0.425 = 0.000
0.000 + x = -2.402836865 + -0.425
x = -2.402836865 + -0.425

Combine like terms: -2.402836865 + -0.425 = -2.827836865
x = -2.827836865

Simplifying
x = -2.827836865


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.977836865, -2.827836865}

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