.1x^2-.2x=1

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Solution for .1x^2-.2x=1 equation:


Simplifying
0.1x2 + -0.2x = 1

Reorder the terms:
-0.2x + 0.1x2 = 1

Solving
-0.2x + 0.1x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -0.2x + 0.1x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -0.2x + 0.1x2 = 0

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

Divide each side by '0.1'.
-10 + -2x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -2x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2x + x2 = 0 + 10
-2x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2x + x2 = 10

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 10 + 1

Reorder the terms:
1 + -2x + x2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2x + x2 = 11

Factor a perfect square on the left side:
(x + -1)(x + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -1 = 3.31662479 Simplifying x + -1 = 3.31662479 Reorder the terms: -1 + x = 3.31662479 Solving -1 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.31662479 + 1 x = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 x = 4.31662479 Simplifying x = 4.31662479

Subproblem 2

x + -1 = -3.31662479 Simplifying x + -1 = -3.31662479 Reorder the terms: -1 + x = -3.31662479 Solving -1 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.31662479 + 1 x = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 x = -2.31662479 Simplifying x = -2.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.31662479, -2.31662479}

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