x^2-4.551x-2.462=0

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Solution for x^2-4.551x-2.462=0 equation: 


Simplifying
x2 + -4.551x + -2.462 = 0

Reorder the terms:
-2.462 + -4.551x + x2 = 0

Solving
-2.462 + -4.551x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.462' to each side of the equation.
-2.462 + -4.551x + 2.462 + x2 = 0 + 2.462

Reorder the terms:
-2.462 + 2.462 + -4.551x + x2 = 0 + 2.462

Combine like terms: -2.462 + 2.462 = 0.000
0.000 + -4.551x + x2 = 0 + 2.462
-4.551x + x2 = 0 + 2.462

Combine like terms: 0 + 2.462 = 2.462
-4.551x + x2 = 2.462

The x term is -4.551x.  Take half its coefficient (-2.2755).
Square it (5.17790025) and add it to both sides.

Add '5.17790025' to each side of the equation.
-4.551x + 5.17790025 + x2 = 2.462 + 5.17790025

Reorder the terms:
5.17790025 + -4.551x + x2 = 2.462 + 5.17790025

Combine like terms: 2.462 + 5.17790025 = 7.63990025
5.17790025 + -4.551x + x2 = 7.63990025

Factor a perfect square on the left side:
(x + -2.2755)(x + -2.2755) = 7.63990025

Calculate the square root of the right side: 2.764036948

Break this problem into two subproblems by setting 
(x + -2.2755) equal to 2.764036948 and -2.764036948.


Subproblem 1
x + -2.2755 = 2.764036948

Simplifying
x + -2.2755 = 2.764036948

Reorder the terms:
-2.2755 + x = 2.764036948

Solving
-2.2755 + x = 2.764036948

Solving for variable 'x'.

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

Add '2.2755' to each side of the equation.
-2.2755 + 2.2755 + x = 2.764036948 + 2.2755

Combine like terms: -2.2755 + 2.2755 = 0.0000
0.0000 + x = 2.764036948 + 2.2755
x = 2.764036948 + 2.2755

Combine like terms: 2.764036948 + 2.2755 = 5.039536948
x = 5.039536948

Simplifying
x = 5.039536948


Subproblem 2
x + -2.2755 = -2.764036948

Simplifying
x + -2.2755 = -2.764036948

Reorder the terms:
-2.2755 + x = -2.764036948

Solving
-2.2755 + x = -2.764036948

Solving for variable 'x'.

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

Add '2.2755' to each side of the equation.
-2.2755 + 2.2755 + x = -2.764036948 + 2.2755

Combine like terms: -2.2755 + 2.2755 = 0.0000
0.0000 + x = -2.764036948 + 2.2755
x = -2.764036948 + 2.2755

Combine like terms: -2.764036948 + 2.2755 = -0.488536948
x = -0.488536948

Simplifying
x = -0.488536948


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.039536948, -0.488536948}

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