13x^2-18x+6=0

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Solution for 13x^2-18x+6=0 equation:


Simplifying
13x2 + -18x + 6 = 0

Reorder the terms:
6 + -18x + 13x2 = 0

Solving
6 + -18x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
0.4615384615 + -1.384615385x + x2 = 0

Move the constant term to the right:

Add '-0.4615384615' to each side of the equation.
0.4615384615 + -1.384615385x + -0.4615384615 + x2 = 0 + -0.4615384615

Reorder the terms:
0.4615384615 + -0.4615384615 + -1.384615385x + x2 = 0 + -0.4615384615

Combine like terms: 0.4615384615 + -0.4615384615 = 0.0000000000
0.0000000000 + -1.384615385x + x2 = 0 + -0.4615384615
-1.384615385x + x2 = 0 + -0.4615384615

Combine like terms: 0 + -0.4615384615 = -0.4615384615
-1.384615385x + x2 = -0.4615384615

The x term is -1.384615385x.  Take half its coefficient (-0.6923076925).
Square it (0.4792899411) and add it to both sides.

Add '0.4792899411' to each side of the equation.
-1.384615385x + 0.4792899411 + x2 = -0.4615384615 + 0.4792899411

Reorder the terms:
0.4792899411 + -1.384615385x + x2 = -0.4615384615 + 0.4792899411

Combine like terms: -0.4615384615 + 0.4792899411 = 0.0177514796
0.4792899411 + -1.384615385x + x2 = 0.0177514796

Factor a perfect square on the left side:
(x + -0.6923076925)(x + -0.6923076925) = 0.0177514796

Calculate the square root of the right side: 0.133234679

Break this problem into two subproblems by setting 
(x + -0.6923076925) equal to 0.133234679 and -0.133234679.

Subproblem 1

x + -0.6923076925 = 0.133234679 Simplifying x + -0.6923076925 = 0.133234679 Reorder the terms: -0.6923076925 + x = 0.133234679 Solving -0.6923076925 + x = 0.133234679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6923076925' to each side of the equation. -0.6923076925 + 0.6923076925 + x = 0.133234679 + 0.6923076925 Combine like terms: -0.6923076925 + 0.6923076925 = 0.0000000000 0.0000000000 + x = 0.133234679 + 0.6923076925 x = 0.133234679 + 0.6923076925 Combine like terms: 0.133234679 + 0.6923076925 = 0.8255423715 x = 0.8255423715 Simplifying x = 0.8255423715

Subproblem 2

x + -0.6923076925 = -0.133234679 Simplifying x + -0.6923076925 = -0.133234679 Reorder the terms: -0.6923076925 + x = -0.133234679 Solving -0.6923076925 + x = -0.133234679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6923076925' to each side of the equation. -0.6923076925 + 0.6923076925 + x = -0.133234679 + 0.6923076925 Combine like terms: -0.6923076925 + 0.6923076925 = 0.0000000000 0.0000000000 + x = -0.133234679 + 0.6923076925 x = -0.133234679 + 0.6923076925 Combine like terms: -0.133234679 + 0.6923076925 = 0.5590730135 x = 0.5590730135 Simplifying x = 0.5590730135

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8255423715, 0.5590730135}

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