x^2-4.05x+0.19=0

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Solution for x^2-4.05x+0.19=0 equation:


Simplifying
x2 + -4.05x + 0.19 = 0

Reorder the terms:
0.19 + -4.05x + x2 = 0

Solving
0.19 + -4.05x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.19' to each side of the equation.
0.19 + -4.05x + -0.19 + x2 = 0 + -0.19

Reorder the terms:
0.19 + -0.19 + -4.05x + x2 = 0 + -0.19

Combine like terms: 0.19 + -0.19 = 0.00
0.00 + -4.05x + x2 = 0 + -0.19
-4.05x + x2 = 0 + -0.19

Combine like terms: 0 + -0.19 = -0.19
-4.05x + x2 = -0.19

The x term is -4.05x.  Take half its coefficient (-2.025).
Square it (4.100625) and add it to both sides.

Add '4.100625' to each side of the equation.
-4.05x + 4.100625 + x2 = -0.19 + 4.100625

Reorder the terms:
4.100625 + -4.05x + x2 = -0.19 + 4.100625

Combine like terms: -0.19 + 4.100625 = 3.910625
4.100625 + -4.05x + x2 = 3.910625

Factor a perfect square on the left side:
(x + -2.025)(x + -2.025) = 3.910625

Calculate the square root of the right side: 1.977530025

Break this problem into two subproblems by setting 
(x + -2.025) equal to 1.977530025 and -1.977530025.

Subproblem 1

x + -2.025 = 1.977530025 Simplifying x + -2.025 = 1.977530025 Reorder the terms: -2.025 + x = 1.977530025 Solving -2.025 + x = 1.977530025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.025' to each side of the equation. -2.025 + 2.025 + x = 1.977530025 + 2.025 Combine like terms: -2.025 + 2.025 = 0.000 0.000 + x = 1.977530025 + 2.025 x = 1.977530025 + 2.025 Combine like terms: 1.977530025 + 2.025 = 4.002530025 x = 4.002530025 Simplifying x = 4.002530025

Subproblem 2

x + -2.025 = -1.977530025 Simplifying x + -2.025 = -1.977530025 Reorder the terms: -2.025 + x = -1.977530025 Solving -2.025 + x = -1.977530025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.025' to each side of the equation. -2.025 + 2.025 + x = -1.977530025 + 2.025 Combine like terms: -2.025 + 2.025 = 0.000 0.000 + x = -1.977530025 + 2.025 x = -1.977530025 + 2.025 Combine like terms: -1.977530025 + 2.025 = 0.047469975 x = 0.047469975 Simplifying x = 0.047469975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.002530025, 0.047469975}

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