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Simplifying 12x2 + 13x = 7 Reorder the terms: 13x + 12x2 = 7 Solving 13x + 12x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 13x + 12x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 13x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5833333333 + 1.083333333x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + 1.083333333x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + 1.083333333x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + 1.083333333x + x2 = 0 + 0.5833333333 1.083333333x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 1.083333333x + x2 = 0.5833333333 The x term is 1.083333333x. Take half its coefficient (0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. 1.083333333x + 0.2934027776 + x2 = 0.5833333333 + 0.2934027776 Reorder the terms: 0.2934027776 + 1.083333333x + x2 = 0.5833333333 + 0.2934027776 Combine like terms: 0.5833333333 + 0.2934027776 = 0.8767361109 0.2934027776 + 1.083333333x + x2 = 0.8767361109 Factor a perfect square on the left side: (x + 0.5416666665)(x + 0.5416666665) = 0.8767361109 Calculate the square root of the right side: 0.936341877 Break this problem into two subproblems by setting (x + 0.5416666665) equal to 0.936341877 and -0.936341877.Subproblem 1
x + 0.5416666665 = 0.936341877 Simplifying x + 0.5416666665 = 0.936341877 Reorder the terms: 0.5416666665 + x = 0.936341877 Solving 0.5416666665 + x = 0.936341877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = 0.936341877 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = 0.936341877 + -0.5416666665 x = 0.936341877 + -0.5416666665 Combine like terms: 0.936341877 + -0.5416666665 = 0.3946752105 x = 0.3946752105 Simplifying x = 0.3946752105Subproblem 2
x + 0.5416666665 = -0.936341877 Simplifying x + 0.5416666665 = -0.936341877 Reorder the terms: 0.5416666665 + x = -0.936341877 Solving 0.5416666665 + x = -0.936341877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5416666665' to each side of the equation. 0.5416666665 + -0.5416666665 + x = -0.936341877 + -0.5416666665 Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000 0.0000000000 + x = -0.936341877 + -0.5416666665 x = -0.936341877 + -0.5416666665 Combine like terms: -0.936341877 + -0.5416666665 = -1.4780085435 x = -1.4780085435 Simplifying x = -1.4780085435Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3946752105, -1.4780085435}
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