0.8=-0.1x^2+2x+1

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Solution for 0.8=-0.1x^2+2x+1 equation:


Simplifying
0.8 = -0.1x2 + 2x + 1

Reorder the terms:
0.8 = 1 + 2x + -0.1x2

Solving
0.8 = 1 + 2x + -0.1x2

Solving for variable 'x'.

Combine like terms: 0.8 + -1 = -0.2
-0.2 + -2x + 0.1x2 = 1 + 2x + -0.1x2 + -1 + -2x + 0.1x2

Reorder the terms:
-0.2 + -2x + 0.1x2 = 1 + -1 + 2x + -2x + -0.1x2 + 0.1x2

Combine like terms: 1 + -1 = 0
-0.2 + -2x + 0.1x2 = 0 + 2x + -2x + -0.1x2 + 0.1x2
-0.2 + -2x + 0.1x2 = 2x + -2x + -0.1x2 + 0.1x2

Combine like terms: 2x + -2x = 0
-0.2 + -2x + 0.1x2 = 0 + -0.1x2 + 0.1x2
-0.2 + -2x + 0.1x2 = -0.1x2 + 0.1x2

Combine like terms: -0.1x2 + 0.1x2 = 0.0
-0.2 + -2x + 0.1x2 = 0.0

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

Divide each side by '0.1'.
-2 + -20x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -20x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -20x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -20x + x2 = 0 + 2
-20x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-20x + x2 = 2

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 2 + 100

Reorder the terms:
100 + -20x + x2 = 2 + 100

Combine like terms: 2 + 100 = 102
100 + -20x + x2 = 102

Factor a perfect square on the left side:
(x + -10)(x + -10) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + -10) equal to 10.099504938 and -10.099504938.

Subproblem 1

x + -10 = 10.099504938 Simplifying x + -10 = 10.099504938 Reorder the terms: -10 + x = 10.099504938 Solving -10 + x = 10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 10.099504938 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.099504938 + 10 x = 10.099504938 + 10 Combine like terms: 10.099504938 + 10 = 20.099504938 x = 20.099504938 Simplifying x = 20.099504938

Subproblem 2

x + -10 = -10.099504938 Simplifying x + -10 = -10.099504938 Reorder the terms: -10 + x = -10.099504938 Solving -10 + x = -10.099504938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -10.099504938 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.099504938 + 10 x = -10.099504938 + 10 Combine like terms: -10.099504938 + 10 = -0.099504938 x = -0.099504938 Simplifying x = -0.099504938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.099504938, -0.099504938}

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