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Simplifying -13x2 + 2x + 6 = 0 Reorder the terms: 6 + 2x + -13x2 = 0 Solving 6 + 2x + -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 + -0.1538461538x + x2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + -0.1538461538x + 0.4615384615 + x2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + -0.1538461538x + x2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + -0.1538461538x + x2 = 0 + 0.4615384615 -0.1538461538x + x2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 -0.1538461538x + x2 = 0.4615384615 The x term is -0.1538461538x. Take half its coefficient (-0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. -0.1538461538x + 0.005917159760 + x2 = 0.4615384615 + 0.005917159760 Reorder the terms: 0.005917159760 + -0.1538461538x + x2 = 0.4615384615 + 0.005917159760 Combine like terms: 0.4615384615 + 0.005917159760 = 0.46745562126 0.005917159760 + -0.1538461538x + x2 = 0.46745562126 Factor a perfect square on the left side: (x + -0.0769230769)(x + -0.0769230769) = 0.46745562126 Calculate the square root of the right side: 0.683707263 Break this problem into two subproblems by setting (x + -0.0769230769) equal to 0.683707263 and -0.683707263.Subproblem 1
x + -0.0769230769 = 0.683707263 Simplifying x + -0.0769230769 = 0.683707263 Reorder the terms: -0.0769230769 + x = 0.683707263 Solving -0.0769230769 + x = 0.683707263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0769230769' to each side of the equation. -0.0769230769 + 0.0769230769 + x = 0.683707263 + 0.0769230769 Combine like terms: -0.0769230769 + 0.0769230769 = 0.0000000000 0.0000000000 + x = 0.683707263 + 0.0769230769 x = 0.683707263 + 0.0769230769 Combine like terms: 0.683707263 + 0.0769230769 = 0.7606303399 x = 0.7606303399 Simplifying x = 0.7606303399Subproblem 2
x + -0.0769230769 = -0.683707263 Simplifying x + -0.0769230769 = -0.683707263 Reorder the terms: -0.0769230769 + x = -0.683707263 Solving -0.0769230769 + x = -0.683707263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0769230769' to each side of the equation. -0.0769230769 + 0.0769230769 + x = -0.683707263 + 0.0769230769 Combine like terms: -0.0769230769 + 0.0769230769 = 0.0000000000 0.0000000000 + x = -0.683707263 + 0.0769230769 x = -0.683707263 + 0.0769230769 Combine like terms: -0.683707263 + 0.0769230769 = -0.6067841861 x = -0.6067841861 Simplifying x = -0.6067841861Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7606303399, -0.6067841861}
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