3-x+40+x(2*x)=54

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Solution for 3-x+40+x(2*x)=54 equation:


Simplifying
3 + -1x + 40 + x(2x) = 54

Remove parenthesis around (2x)
3 + -1x + 40 + x * 2x = 54

Reorder the terms for easier multiplication:
3 + -1x + 40 + 2x * x = 54

Multiply x * x
3 + -1x + 40 + 2x2 = 54

Reorder the terms:
3 + 40 + -1x + 2x2 = 54

Combine like terms: 3 + 40 = 43
43 + -1x + 2x2 = 54

Solving
43 + -1x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
43 + -54 + -1x + 2x2 = 54 + -54

Combine like terms: 43 + -54 = -11
-11 + -1x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-11 + -1x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -0.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -0.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -0.5x + x2 = 0 + 5.5
-0.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-0.5x + x2 = 5.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 5.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 5.5 + 0.0625

Combine like terms: 5.5 + 0.0625 = 5.5625
0.0625 + -0.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.358495283 and -2.358495283.

Subproblem 1

x + -0.25 = 2.358495283 Simplifying x + -0.25 = 2.358495283 Reorder the terms: -0.25 + x = 2.358495283 Solving -0.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.358495283 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.358495283 + 0.25 x = 2.358495283 + 0.25 Combine like terms: 2.358495283 + 0.25 = 2.608495283 x = 2.608495283 Simplifying x = 2.608495283

Subproblem 2

x + -0.25 = -2.358495283 Simplifying x + -0.25 = -2.358495283 Reorder the terms: -0.25 + x = -2.358495283 Solving -0.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.358495283 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.358495283 + 0.25 x = -2.358495283 + 0.25 Combine like terms: -2.358495283 + 0.25 = -2.108495283 x = -2.108495283 Simplifying x = -2.108495283

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.608495283, -2.108495283}

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