1=5.5x-4.9(x^2)

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Solution for 1=5.5x-4.9(x^2) equation:


Simplifying
1 = 5.5x + -4.9(x2)

Solving
1 = 5.5x + -4.9x2

Solving for variable 'x'.

Reorder the terms:
1 + -5.5x + 4.9x2 = 5.5x + -5.5x + -4.9x2 + 4.9x2

Combine like terms: 5.5x + -5.5x = 0.0
1 + -5.5x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2
1 + -5.5x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
1 + -5.5x + 4.9x2 = 0.0

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

Divide each side by '4.9'.
0.2040816327 + -1.12244898x + x2 = 0

Move the constant term to the right:

Add '-0.2040816327' to each side of the equation.
0.2040816327 + -1.12244898x + -0.2040816327 + x2 = 0 + -0.2040816327

Reorder the terms:
0.2040816327 + -0.2040816327 + -1.12244898x + x2 = 0 + -0.2040816327

Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000
0.0000000000 + -1.12244898x + x2 = 0 + -0.2040816327
-1.12244898x + x2 = 0 + -0.2040816327

Combine like terms: 0 + -0.2040816327 = -0.2040816327
-1.12244898x + x2 = -0.2040816327

The x term is -1.12244898x.  Take half its coefficient (-0.56122449).
Square it (0.3149729282) and add it to both sides.

Add '0.3149729282' to each side of the equation.
-1.12244898x + 0.3149729282 + x2 = -0.2040816327 + 0.3149729282

Reorder the terms:
0.3149729282 + -1.12244898x + x2 = -0.2040816327 + 0.3149729282

Combine like terms: -0.2040816327 + 0.3149729282 = 0.1108912955
0.3149729282 + -1.12244898x + x2 = 0.1108912955

Factor a perfect square on the left side:
(x + -0.56122449)(x + -0.56122449) = 0.1108912955

Calculate the square root of the right side: 0.333003447

Break this problem into two subproblems by setting 
(x + -0.56122449) equal to 0.333003447 and -0.333003447.

Subproblem 1

x + -0.56122449 = 0.333003447 Simplifying x + -0.56122449 = 0.333003447 Reorder the terms: -0.56122449 + x = 0.333003447 Solving -0.56122449 + x = 0.333003447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + x = 0.333003447 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + x = 0.333003447 + 0.56122449 x = 0.333003447 + 0.56122449 Combine like terms: 0.333003447 + 0.56122449 = 0.894227937 x = 0.894227937 Simplifying x = 0.894227937

Subproblem 2

x + -0.56122449 = -0.333003447 Simplifying x + -0.56122449 = -0.333003447 Reorder the terms: -0.56122449 + x = -0.333003447 Solving -0.56122449 + x = -0.333003447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.56122449' to each side of the equation. -0.56122449 + 0.56122449 + x = -0.333003447 + 0.56122449 Combine like terms: -0.56122449 + 0.56122449 = 0.00000000 0.00000000 + x = -0.333003447 + 0.56122449 x = -0.333003447 + 0.56122449 Combine like terms: -0.333003447 + 0.56122449 = 0.228221043 x = 0.228221043 Simplifying x = 0.228221043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.894227937, 0.228221043}

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