1-1.8x+0.81x^2=0

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Solution for 1-1.8x+0.81x^2=0 equation:


Simplifying
1 + -1.8x + 0.81x2 = 0

Solving
1 + -1.8x + 0.81x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.81 the coefficient of the squared term: 

Divide each side by '0.81'.
1.234567901 + -2.222222222x + x2 = 0

Move the constant term to the right:

Add '-1.234567901' to each side of the equation.
1.234567901 + -2.222222222x + -1.234567901 + x2 = 0 + -1.234567901

Reorder the terms:
1.234567901 + -1.234567901 + -2.222222222x + x2 = 0 + -1.234567901

Combine like terms: 1.234567901 + -1.234567901 = 0.000000000
0.000000000 + -2.222222222x + x2 = 0 + -1.234567901
-2.222222222x + x2 = 0 + -1.234567901

Combine like terms: 0 + -1.234567901 = -1.234567901
-2.222222222x + x2 = -1.234567901

The x term is -2.222222222x.  Take half its coefficient (-1.111111111).
Square it (1.234567901) and add it to both sides.

Add '1.234567901' to each side of the equation.
-2.222222222x + 1.234567901 + x2 = -1.234567901 + 1.234567901

Reorder the terms:
1.234567901 + -2.222222222x + x2 = -1.234567901 + 1.234567901

Combine like terms: -1.234567901 + 1.234567901 = 0.000000000
1.234567901 + -2.222222222x + x2 = 0.000000000

Factor a perfect square on the left side:
(x + -1.111111111)(x + -1.111111111) = 0.000000000

Calculate the square root of the right side: 0.000000000

Break this problem into two subproblems by setting 
(x + -1.111111111) equal to 0.000000000 and 0.000000000.

Subproblem 1

x + -1.111111111 = 0.000000000 Simplifying x + -1.111111111 = 0.000000000 Reorder the terms: -1.111111111 + x = 0.000000000 Solving -1.111111111 + x = 0.000000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = 0.000000000 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 0.000000000 + 1.111111111 x = 0.000000000 + 1.111111111 Combine like terms: 0.000000000 + 1.111111111 = 1.111111111 x = 1.111111111 Simplifying x = 1.111111111

Subproblem 2

x + -1.111111111 = 0.000000000 Simplifying x + -1.111111111 = 0.000000000 Reorder the terms: -1.111111111 + x = 0.000000000 Solving -1.111111111 + x = 0.000000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = 0.000000000 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 0.000000000 + 1.111111111 x = 0.000000000 + 1.111111111 Combine like terms: 0.000000000 + 1.111111111 = 1.111111111 x = 1.111111111 Simplifying x = 1.111111111

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.111111111, 1.111111111}

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