x^2+1.05x-1.096=0

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Solution for x^2+1.05x-1.096=0 equation:


Simplifying
x2 + 1.05x + -1.096 = 0

Reorder the terms:
-1.096 + 1.05x + x2 = 0

Solving
-1.096 + 1.05x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.096' to each side of the equation.
-1.096 + 1.05x + 1.096 + x2 = 0 + 1.096

Reorder the terms:
-1.096 + 1.096 + 1.05x + x2 = 0 + 1.096

Combine like terms: -1.096 + 1.096 = 0.000
0.000 + 1.05x + x2 = 0 + 1.096
1.05x + x2 = 0 + 1.096

Combine like terms: 0 + 1.096 = 1.096
1.05x + x2 = 1.096

The x term is 1.05x.  Take half its coefficient (0.525).
Square it (0.275625) and add it to both sides.

Add '0.275625' to each side of the equation.
1.05x + 0.275625 + x2 = 1.096 + 0.275625

Reorder the terms:
0.275625 + 1.05x + x2 = 1.096 + 0.275625

Combine like terms: 1.096 + 0.275625 = 1.371625
0.275625 + 1.05x + x2 = 1.371625

Factor a perfect square on the left side:
(x + 0.525)(x + 0.525) = 1.371625

Calculate the square root of the right side: 1.171163951

Break this problem into two subproblems by setting 
(x + 0.525) equal to 1.171163951 and -1.171163951.

Subproblem 1

x + 0.525 = 1.171163951 Simplifying x + 0.525 = 1.171163951 Reorder the terms: 0.525 + x = 1.171163951 Solving 0.525 + x = 1.171163951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = 1.171163951 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 1.171163951 + -0.525 x = 1.171163951 + -0.525 Combine like terms: 1.171163951 + -0.525 = 0.646163951 x = 0.646163951 Simplifying x = 0.646163951

Subproblem 2

x + 0.525 = -1.171163951 Simplifying x + 0.525 = -1.171163951 Reorder the terms: 0.525 + x = -1.171163951 Solving 0.525 + x = -1.171163951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = -1.171163951 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -1.171163951 + -0.525 x = -1.171163951 + -0.525 Combine like terms: -1.171163951 + -0.525 = -1.696163951 x = -1.696163951 Simplifying x = -1.696163951

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.646163951, -1.696163951}

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