-x^2+2.1x=-0.2

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Solution for -x^2+2.1x=-0.2 equation:


Simplifying
-1x2 + 2.1x = -0.2

Reorder the terms:
2.1x + -1x2 = -0.2

Solving
2.1x + -1x2 = -0.2

Solving for variable 'x'.

Reorder the terms:
0.2 + 2.1x + -1x2 = -0.2 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.2 + 2.1x + -1x2 = 0.0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.2 + -2.1x + x2 = 0.0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -2.1x + 0.2 + x2 = 0.0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -2.1x + x2 = 0.0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -2.1x + x2 = 0.0 + 0.2
-2.1x + x2 = 0.0 + 0.2

Combine like terms: 0.0 + 0.2 = 0.2
-2.1x + x2 = 0.2

The x term is -2.1x.  Take half its coefficient (-1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
-2.1x + 1.1025 + x2 = 0.2 + 1.1025

Reorder the terms:
1.1025 + -2.1x + x2 = 0.2 + 1.1025

Combine like terms: 0.2 + 1.1025 = 1.3025
1.1025 + -2.1x + x2 = 1.3025

Factor a perfect square on the left side:
(x + -1.05)(x + -1.05) = 1.3025

Calculate the square root of the right side: 1.141271221

Break this problem into two subproblems by setting 
(x + -1.05) equal to 1.141271221 and -1.141271221.

Subproblem 1

x + -1.05 = 1.141271221 Simplifying x + -1.05 = 1.141271221 Reorder the terms: -1.05 + x = 1.141271221 Solving -1.05 + x = 1.141271221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = 1.141271221 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = 1.141271221 + 1.05 x = 1.141271221 + 1.05 Combine like terms: 1.141271221 + 1.05 = 2.191271221 x = 2.191271221 Simplifying x = 2.191271221

Subproblem 2

x + -1.05 = -1.141271221 Simplifying x + -1.05 = -1.141271221 Reorder the terms: -1.05 + x = -1.141271221 Solving -1.05 + x = -1.141271221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = -1.141271221 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = -1.141271221 + 1.05 x = -1.141271221 + 1.05 Combine like terms: -1.141271221 + 1.05 = -0.091271221 x = -0.091271221 Simplifying x = -0.091271221

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.191271221, -0.091271221}

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