x^2-1.8x+0.81=0

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


Simplifying
x2 + -1.8x + 0.81 = 0

Reorder the terms:
0.81 + -1.8x + x2 = 0

Solving
0.81 + -1.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.81' to each side of the equation.
0.81 + -1.8x + -0.81 + x2 = 0 + -0.81

Reorder the terms:
0.81 + -0.81 + -1.8x + x2 = 0 + -0.81

Combine like terms: 0.81 + -0.81 = 0.00
0.00 + -1.8x + x2 = 0 + -0.81
-1.8x + x2 = 0 + -0.81

Combine like terms: 0 + -0.81 = -0.81
-1.8x + x2 = -0.81

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = -0.81 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -0.81 + 0.81

Combine like terms: -0.81 + 0.81 = 0.00
0.81 + -1.8x + x2 = 0.00

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -0.9) equal to 0.00 and 0.00.

Subproblem 1

x + -0.9 = 0.00 Simplifying x + -0.9 = 0.00 Reorder the terms: -0.9 + x = 0.00 Solving -0.9 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.00 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.00 + 0.9 x = 0.00 + 0.9 Combine like terms: 0.00 + 0.9 = 0.9 x = 0.9 Simplifying x = 0.9

Subproblem 2

x + -0.9 = 0.00 Simplifying x + -0.9 = 0.00 Reorder the terms: -0.9 + x = 0.00 Solving -0.9 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.00 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.00 + 0.9 x = 0.00 + 0.9 Combine like terms: 0.00 + 0.9 = 0.9 x = 0.9 Simplifying x = 0.9

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9, 0.9}

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