X^2+4.142X-4.289=0

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Solution for X^2+4.142X-4.289=0 equation: 


Simplifying
X2 + 4.142X + -4.289 = 0

Reorder the terms:
-4.289 + 4.142X + X2 = 0

Solving
-4.289 + 4.142X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '4.289' to each side of the equation.
-4.289 + 4.142X + 4.289 + X2 = 0 + 4.289

Reorder the terms:
-4.289 + 4.289 + 4.142X + X2 = 0 + 4.289

Combine like terms: -4.289 + 4.289 = 0.000
0.000 + 4.142X + X2 = 0 + 4.289
4.142X + X2 = 0 + 4.289

Combine like terms: 0 + 4.289 = 4.289
4.142X + X2 = 4.289

The X term is 4.142X.  Take half its coefficient (2.071).
Square it (4.289041) and add it to both sides.

Add '4.289041' to each side of the equation.
4.142X + 4.289041 + X2 = 4.289 + 4.289041

Reorder the terms:
4.289041 + 4.142X + X2 = 4.289 + 4.289041

Combine like terms: 4.289 + 4.289041 = 8.578041
4.289041 + 4.142X + X2 = 8.578041

Factor a perfect square on the left side:
(X + 2.071)(X + 2.071) = 8.578041

Calculate the square root of the right side: 2.928829288

Break this problem into two subproblems by setting 
(X + 2.071) equal to 2.928829288 and -2.928829288.


Subproblem 1
X + 2.071 = 2.928829288

Simplifying
X + 2.071 = 2.928829288

Reorder the terms:
2.071 + X = 2.928829288

Solving
2.071 + X = 2.928829288

Solving for variable 'X'.

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

Add '-2.071' to each side of the equation.
2.071 + -2.071 + X = 2.928829288 + -2.071

Combine like terms: 2.071 + -2.071 = 0.000
0.000 + X = 2.928829288 + -2.071
X = 2.928829288 + -2.071

Combine like terms: 2.928829288 + -2.071 = 0.857829288
X = 0.857829288

Simplifying
X = 0.857829288


Subproblem 2
X + 2.071 = -2.928829288

Simplifying
X + 2.071 = -2.928829288

Reorder the terms:
2.071 + X = -2.928829288

Solving
2.071 + X = -2.928829288

Solving for variable 'X'.

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

Add '-2.071' to each side of the equation.
2.071 + -2.071 + X = -2.928829288 + -2.071

Combine like terms: 2.071 + -2.071 = 0.000
0.000 + X = -2.928829288 + -2.071
X = -2.928829288 + -2.071

Combine like terms: -2.928829288 + -2.071 = -4.999829288
X = -4.999829288

Simplifying
X = -4.999829288


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.857829288, -4.999829288}

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