92x*27(3-x)=0.11

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Solution for 92x*27(3-x)=0.11 equation:


Simplifying
92x * 27(3 + -1x) = 0.11

Reorder the terms for easier multiplication:
92 * 27x(3 + -1x) = 0.11

Multiply 92 * 27
2484x(3 + -1x) = 0.11
(3 * 2484x + -1x * 2484x) = 0.11
(7452x + -2484x2) = 0.11

Solving
7452x + -2484x2 = 0.11

Solving for variable 'x'.

Reorder the terms:
-0.11 + 7452x + -2484x2 = 0.11 + -0.11

Combine like terms: 0.11 + -0.11 = 0.00
-0.11 + 7452x + -2484x2 = 0.00

Begin completing the square.  Divide all terms by
-2484 the coefficient of the squared term: 

Divide each side by '-2484'.
0.00004428341385 + -3x + x2 = 0.00

Move the constant term to the right:

Add '-0.00004428341385' to each side of the equation.
0.00004428341385 + -3x + -0.00004428341385 + x2 = 0.00 + -0.00004428341385

Reorder the terms:
0.00004428341385 + -0.00004428341385 + -3x + x2 = 0.00 + -0.00004428341385

Combine like terms: 0.00004428341385 + -0.00004428341385 = 0.00000000000000
0.00000000000000 + -3x + x2 = 0.00 + -0.00004428341385
-3x + x2 = 0.00 + -0.00004428341385

Combine like terms: 0.00 + -0.00004428341385 = -0.00004428341385
-3x + x2 = -0.00004428341385

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -0.00004428341385 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.00004428341385 + 2.25

Combine like terms: -0.00004428341385 + 2.25 = 2.24995571658615
2.25 + -3x + x2 = 2.24995571658615

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2.24995571658615

Calculate the square root of the right side: 1.499985239

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.499985239 and -1.499985239.

Subproblem 1

x + -1.5 = 1.499985239 Simplifying x + -1.5 = 1.499985239 Reorder the terms: -1.5 + x = 1.499985239 Solving -1.5 + x = 1.499985239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.499985239 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.499985239 + 1.5 x = 1.499985239 + 1.5 Combine like terms: 1.499985239 + 1.5 = 2.999985239 x = 2.999985239 Simplifying x = 2.999985239

Subproblem 2

x + -1.5 = -1.499985239 Simplifying x + -1.5 = -1.499985239 Reorder the terms: -1.5 + x = -1.499985239 Solving -1.5 + x = -1.499985239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.499985239 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.499985239 + 1.5 x = -1.499985239 + 1.5 Combine like terms: -1.499985239 + 1.5 = 0.000014761 x = 0.000014761 Simplifying x = 0.000014761

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.999985239, 0.000014761}

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