.5x^2=0.2x+1

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Solution for .5x^2=0.2x+1 equation:


Simplifying
0.5x2 = 0.2x + 1

Reorder the terms:
0.5x2 = 1 + 0.2x

Solving
0.5x2 = 1 + 0.2x

Solving for variable 'x'.

Reorder the terms:
-1 + -0.2x + 0.5x2 = 1 + 0.2x + -1 + -0.2x

Reorder the terms:
-1 + -0.2x + 0.5x2 = 1 + -1 + 0.2x + -0.2x

Combine like terms: 1 + -1 = 0
-1 + -0.2x + 0.5x2 = 0 + 0.2x + -0.2x
-1 + -0.2x + 0.5x2 = 0.2x + -0.2x

Combine like terms: 0.2x + -0.2x = 0.0
-1 + -0.2x + 0.5x2 = 0.0

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

Divide each side by '0.5'.
-2 + -0.4x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.4x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.4x + x2 = 0 + 2
-0.4x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.4x + x2 = 2

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 2 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 2 + 0.04

Combine like terms: 2 + 0.04 = 2.04
0.04 + -0.4x + x2 = 2.04

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 2.04

Calculate the square root of the right side: 1.428285686

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.428285686 and -1.428285686.

Subproblem 1

x + -0.2 = 1.428285686 Simplifying x + -0.2 = 1.428285686 Reorder the terms: -0.2 + x = 1.428285686 Solving -0.2 + x = 1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.428285686 + 0.2 x = 1.428285686 + 0.2 Combine like terms: 1.428285686 + 0.2 = 1.628285686 x = 1.628285686 Simplifying x = 1.628285686

Subproblem 2

x + -0.2 = -1.428285686 Simplifying x + -0.2 = -1.428285686 Reorder the terms: -0.2 + x = -1.428285686 Solving -0.2 + x = -1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.428285686 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.428285686 + 0.2 x = -1.428285686 + 0.2 Combine like terms: -1.428285686 + 0.2 = -1.228285686 x = -1.228285686 Simplifying x = -1.228285686

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.628285686, -1.228285686}

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