4x-4x^2-0.3=0

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Solution for 4x-4x^2-0.3=0 equation:


Simplifying
4x + -4x2 + -0.3 = 0

Reorder the terms:
-0.3 + 4x + -4x2 = 0

Solving
-0.3 + 4x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.075 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.075' to each side of the equation.
0.075 + -1x + -0.075 + x2 = 0 + -0.075

Reorder the terms:
0.075 + -0.075 + -1x + x2 = 0 + -0.075

Combine like terms: 0.075 + -0.075 = 0.000
0.000 + -1x + x2 = 0 + -0.075
-1x + x2 = 0 + -0.075

Combine like terms: 0 + -0.075 = -0.075
-1x + x2 = -0.075

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.075 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.075 + 0.25

Combine like terms: -0.075 + 0.25 = 0.175
0.25 + -1x + x2 = 0.175

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.175

Calculate the square root of the right side: 0.418330013

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.418330013 and -0.418330013.

Subproblem 1

x + -0.5 = 0.418330013 Simplifying x + -0.5 = 0.418330013 Reorder the terms: -0.5 + x = 0.418330013 Solving -0.5 + x = 0.418330013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.418330013 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.418330013 + 0.5 x = 0.418330013 + 0.5 Combine like terms: 0.418330013 + 0.5 = 0.918330013 x = 0.918330013 Simplifying x = 0.918330013

Subproblem 2

x + -0.5 = -0.418330013 Simplifying x + -0.5 = -0.418330013 Reorder the terms: -0.5 + x = -0.418330013 Solving -0.5 + x = -0.418330013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.418330013 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.418330013 + 0.5 x = -0.418330013 + 0.5 Combine like terms: -0.418330013 + 0.5 = 0.081669987 x = 0.081669987 Simplifying x = 0.081669987

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.918330013, 0.081669987}

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