4.20=4x^2-8x+4

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Solution for 4.20=4x^2-8x+4 equation:


Simplifying
4.20 = 4x2 + -8x + 4

Reorder the terms:
4.20 = 4 + -8x + 4x2

Solving
4.20 = 4 + -8x + 4x2

Solving for variable 'x'.

Combine like terms: 4.20 + -4 = 0.2
0.2 + 8x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2

Reorder the terms:
0.2 + 8x + -4x2 = 4 + -4 + -8x + 8x + 4x2 + -4x2

Combine like terms: 4 + -4 = 0
0.2 + 8x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2
0.2 + 8x + -4x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
0.2 + 8x + -4x2 = 0 + 4x2 + -4x2
0.2 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
0.2 + 8x + -4x2 = 0

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

Divide each side by '-4'.
-0.05 + -2x + x2 = 0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -2x + 0.05 + x2 = 0 + 0.05

Reorder the terms:
-0.05 + 0.05 + -2x + x2 = 0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -2x + x2 = 0 + 0.05
-2x + x2 = 0 + 0.05

Combine like terms: 0 + 0.05 = 0.05
-2x + x2 = 0.05

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 = 0.05 + 1

Reorder the terms:
1 + -2x + x2 = 0.05 + 1

Combine like terms: 0.05 + 1 = 1.05
1 + -2x + x2 = 1.05

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.05

Calculate the square root of the right side: 1.024695077

Break this problem into two subproblems by setting 
(x + -1) equal to 1.024695077 and -1.024695077.

Subproblem 1

x + -1 = 1.024695077 Simplifying x + -1 = 1.024695077 Reorder the terms: -1 + x = 1.024695077 Solving -1 + x = 1.024695077 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 = 1.024695077 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.024695077 + 1 x = 1.024695077 + 1 Combine like terms: 1.024695077 + 1 = 2.024695077 x = 2.024695077 Simplifying x = 2.024695077

Subproblem 2

x + -1 = -1.024695077 Simplifying x + -1 = -1.024695077 Reorder the terms: -1 + x = -1.024695077 Solving -1 + x = -1.024695077 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 = -1.024695077 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.024695077 + 1 x = -1.024695077 + 1 Combine like terms: -1.024695077 + 1 = -0.024695077 x = -0.024695077 Simplifying x = -0.024695077

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.024695077, -0.024695077}

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