x^2-5.02x-5.57959=0

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Solution for x^2-5.02x-5.57959=0 equation: 


Simplifying
x2 + -5.02x + -5.57959 = 0

Reorder the terms:
-5.57959 + -5.02x + x2 = 0

Solving
-5.57959 + -5.02x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5.57959' to each side of the equation.
-5.57959 + -5.02x + 5.57959 + x2 = 0 + 5.57959

Reorder the terms:
-5.57959 + 5.57959 + -5.02x + x2 = 0 + 5.57959

Combine like terms: -5.57959 + 5.57959 = 0.00000
0.00000 + -5.02x + x2 = 0 + 5.57959
-5.02x + x2 = 0 + 5.57959

Combine like terms: 0 + 5.57959 = 5.57959
-5.02x + x2 = 5.57959

The x term is -5.02x.  Take half its coefficient (-2.51).
Square it (6.3001) and add it to both sides.

Add '6.3001' to each side of the equation.
-5.02x + 6.3001 + x2 = 5.57959 + 6.3001

Reorder the terms:
6.3001 + -5.02x + x2 = 5.57959 + 6.3001

Combine like terms: 5.57959 + 6.3001 = 11.87969
6.3001 + -5.02x + x2 = 11.87969

Factor a perfect square on the left side:
(x + -2.51)(x + -2.51) = 11.87969

Calculate the square root of the right side: 3.446692618

Break this problem into two subproblems by setting 
(x + -2.51) equal to 3.446692618 and -3.446692618.


Subproblem 1
x + -2.51 = 3.446692618

Simplifying
x + -2.51 = 3.446692618

Reorder the terms:
-2.51 + x = 3.446692618

Solving
-2.51 + x = 3.446692618

Solving for variable 'x'.

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

Add '2.51' to each side of the equation.
-2.51 + 2.51 + x = 3.446692618 + 2.51

Combine like terms: -2.51 + 2.51 = 0.00
0.00 + x = 3.446692618 + 2.51
x = 3.446692618 + 2.51

Combine like terms: 3.446692618 + 2.51 = 5.956692618
x = 5.956692618

Simplifying
x = 5.956692618


Subproblem 2
x + -2.51 = -3.446692618

Simplifying
x + -2.51 = -3.446692618

Reorder the terms:
-2.51 + x = -3.446692618

Solving
-2.51 + x = -3.446692618

Solving for variable 'x'.

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

Add '2.51' to each side of the equation.
-2.51 + 2.51 + x = -3.446692618 + 2.51

Combine like terms: -2.51 + 2.51 = 0.00
0.00 + x = -3.446692618 + 2.51
x = -3.446692618 + 2.51

Combine like terms: -3.446692618 + 2.51 = -0.936692618
x = -0.936692618

Simplifying
x = -0.936692618


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.956692618, -0.936692618}

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