0=x^2-1.4x+0.2

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Solution for 0=x^2-1.4x+0.2 equation:


Simplifying
0 = x2 + -1.4x + 0.2

Reorder the terms:
0 = 0.2 + -1.4x + x2

Solving
0 = 0.2 + -1.4x + x2

Solving for variable 'x'.

Combine like terms: 0 + -0.2 = -0.2
-0.2 + 1.4x + -1x2 = 0.2 + -1.4x + x2 + -0.2 + 1.4x + -1x2

Reorder the terms:
-0.2 + 1.4x + -1x2 = 0.2 + -0.2 + -1.4x + 1.4x + x2 + -1x2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + 1.4x + -1x2 = 0.0 + -1.4x + 1.4x + x2 + -1x2
-0.2 + 1.4x + -1x2 = -1.4x + 1.4x + x2 + -1x2

Combine like terms: -1.4x + 1.4x = 0.0
-0.2 + 1.4x + -1x2 = 0.0 + x2 + -1x2
-0.2 + 1.4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-0.2 + 1.4x + -1x2 = 0

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

Divide each side by '-1'.
0.2 + -1.4x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.4x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.4x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.4x + x2 = 0 + -0.2
-1.4x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.4x + x2 = -0.2

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = -0.2 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = -0.2 + 0.49

Combine like terms: -0.2 + 0.49 = 0.29
0.49 + -1.4x + x2 = 0.29

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(x + -0.7) equal to 0.538516481 and -0.538516481.

Subproblem 1

x + -0.7 = 0.538516481 Simplifying x + -0.7 = 0.538516481 Reorder the terms: -0.7 + x = 0.538516481 Solving -0.7 + x = 0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.538516481 + 0.7 x = 0.538516481 + 0.7 Combine like terms: 0.538516481 + 0.7 = 1.238516481 x = 1.238516481 Simplifying x = 1.238516481

Subproblem 2

x + -0.7 = -0.538516481 Simplifying x + -0.7 = -0.538516481 Reorder the terms: -0.7 + x = -0.538516481 Solving -0.7 + x = -0.538516481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.538516481 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.538516481 + 0.7 x = -0.538516481 + 0.7 Combine like terms: -0.538516481 + 0.7 = 0.161483519 x = 0.161483519 Simplifying x = 0.161483519

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.238516481, 0.161483519}

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