x^2-2.05x+1.0445=0

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Solution for x^2-2.05x+1.0445=0 equation:


Simplifying
x2 + -2.05x + 1.0445 = 0

Reorder the terms:
1.0445 + -2.05x + x2 = 0

Solving
1.0445 + -2.05x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.0445' to each side of the equation.
1.0445 + -2.05x + -1.0445 + x2 = 0 + -1.0445

Reorder the terms:
1.0445 + -1.0445 + -2.05x + x2 = 0 + -1.0445

Combine like terms: 1.0445 + -1.0445 = 0.0000
0.0000 + -2.05x + x2 = 0 + -1.0445
-2.05x + x2 = 0 + -1.0445

Combine like terms: 0 + -1.0445 = -1.0445
-2.05x + x2 = -1.0445

The x term is -2.05x.  Take half its coefficient (-1.025).
Square it (1.050625) and add it to both sides.

Add '1.050625' to each side of the equation.
-2.05x + 1.050625 + x2 = -1.0445 + 1.050625

Reorder the terms:
1.050625 + -2.05x + x2 = -1.0445 + 1.050625

Combine like terms: -1.0445 + 1.050625 = 0.006125
1.050625 + -2.05x + x2 = 0.006125

Factor a perfect square on the left side:
(x + -1.025)(x + -1.025) = 0.006125

Calculate the square root of the right side: 0.078262379

Break this problem into two subproblems by setting 
(x + -1.025) equal to 0.078262379 and -0.078262379.

Subproblem 1

x + -1.025 = 0.078262379 Simplifying x + -1.025 = 0.078262379 Reorder the terms: -1.025 + x = 0.078262379 Solving -1.025 + x = 0.078262379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.025' to each side of the equation. -1.025 + 1.025 + x = 0.078262379 + 1.025 Combine like terms: -1.025 + 1.025 = 0.000 0.000 + x = 0.078262379 + 1.025 x = 0.078262379 + 1.025 Combine like terms: 0.078262379 + 1.025 = 1.103262379 x = 1.103262379 Simplifying x = 1.103262379

Subproblem 2

x + -1.025 = -0.078262379 Simplifying x + -1.025 = -0.078262379 Reorder the terms: -1.025 + x = -0.078262379 Solving -1.025 + x = -0.078262379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.025' to each side of the equation. -1.025 + 1.025 + x = -0.078262379 + 1.025 Combine like terms: -1.025 + 1.025 = 0.000 0.000 + x = -0.078262379 + 1.025 x = -0.078262379 + 1.025 Combine like terms: -0.078262379 + 1.025 = 0.946737621 x = 0.946737621 Simplifying x = 0.946737621

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.103262379, 0.946737621}

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