12x^2=18x-1

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Solution for 12x^2=18x-1 equation:


Simplifying
12x2 = 18x + -1

Reorder the terms:
12x2 = -1 + 18x

Solving
12x2 = -1 + 18x

Solving for variable 'x'.

Reorder the terms:
1 + -18x + 12x2 = -1 + 18x + 1 + -18x

Reorder the terms:
1 + -18x + 12x2 = -1 + 1 + 18x + -18x

Combine like terms: -1 + 1 = 0
1 + -18x + 12x2 = 0 + 18x + -18x
1 + -18x + 12x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
1 + -18x + 12x2 = 0

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

Divide each side by '12'.
0.08333333333 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-0.08333333333' to each side of the equation.
0.08333333333 + -1.5x + -0.08333333333 + x2 = 0 + -0.08333333333

Reorder the terms:
0.08333333333 + -0.08333333333 + -1.5x + x2 = 0 + -0.08333333333

Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000
0.00000000000 + -1.5x + x2 = 0 + -0.08333333333
-1.5x + x2 = 0 + -0.08333333333

Combine like terms: 0 + -0.08333333333 = -0.08333333333
-1.5x + x2 = -0.08333333333

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.08333333333 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.08333333333 + 0.5625

Combine like terms: -0.08333333333 + 0.5625 = 0.47916666667
0.5625 + -1.5x + x2 = 0.47916666667

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.47916666667

Calculate the square root of the right side: 0.692218655

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.692218655 and -0.692218655.

Subproblem 1

x + -0.75 = 0.692218655 Simplifying x + -0.75 = 0.692218655 Reorder the terms: -0.75 + x = 0.692218655 Solving -0.75 + x = 0.692218655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.692218655 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.692218655 + 0.75 x = 0.692218655 + 0.75 Combine like terms: 0.692218655 + 0.75 = 1.442218655 x = 1.442218655 Simplifying x = 1.442218655

Subproblem 2

x + -0.75 = -0.692218655 Simplifying x + -0.75 = -0.692218655 Reorder the terms: -0.75 + x = -0.692218655 Solving -0.75 + x = -0.692218655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.692218655 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.692218655 + 0.75 x = -0.692218655 + 0.75 Combine like terms: -0.692218655 + 0.75 = 0.057781345 x = 0.057781345 Simplifying x = 0.057781345

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.442218655, 0.057781345}

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