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Simplifying 1.14x2 + -14.6 = 1.45x Reorder the terms: -14.6 + 1.14x2 = 1.45x Solving -14.6 + 1.14x2 = 1.45x Solving for variable 'x'. Reorder the terms: -14.6 + -1.45x + 1.14x2 = 1.45x + -1.45x Combine like terms: 1.45x + -1.45x = 0.00 -14.6 + -1.45x + 1.14x2 = 0.00 Begin completing the square. Divide all terms by 1.14 the coefficient of the squared term: Divide each side by '1.14'. -12.80701754 + -1.271929825x + x2 = 0 Move the constant term to the right: Add '12.80701754' to each side of the equation. -12.80701754 + -1.271929825x + 12.80701754 + x2 = 0 + 12.80701754 Reorder the terms: -12.80701754 + 12.80701754 + -1.271929825x + x2 = 0 + 12.80701754 Combine like terms: -12.80701754 + 12.80701754 = 0.00000000 0.00000000 + -1.271929825x + x2 = 0 + 12.80701754 -1.271929825x + x2 = 0 + 12.80701754 Combine like terms: 0 + 12.80701754 = 12.80701754 -1.271929825x + x2 = 12.80701754 The x term is -1.271929825x. Take half its coefficient (-0.6359649125). Square it (0.4044513699) and add it to both sides. Add '0.4044513699' to each side of the equation. -1.271929825x + 0.4044513699 + x2 = 12.80701754 + 0.4044513699 Reorder the terms: 0.4044513699 + -1.271929825x + x2 = 12.80701754 + 0.4044513699 Combine like terms: 12.80701754 + 0.4044513699 = 13.2114689099 0.4044513699 + -1.271929825x + x2 = 13.2114689099 Factor a perfect square on the left side: (x + -0.6359649125)(x + -0.6359649125) = 13.2114689099 Calculate the square root of the right side: 3.634758439 Break this problem into two subproblems by setting (x + -0.6359649125) equal to 3.634758439 and -3.634758439.Subproblem 1
x + -0.6359649125 = 3.634758439 Simplifying x + -0.6359649125 = 3.634758439 Reorder the terms: -0.6359649125 + x = 3.634758439 Solving -0.6359649125 + x = 3.634758439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6359649125' to each side of the equation. -0.6359649125 + 0.6359649125 + x = 3.634758439 + 0.6359649125 Combine like terms: -0.6359649125 + 0.6359649125 = 0.0000000000 0.0000000000 + x = 3.634758439 + 0.6359649125 x = 3.634758439 + 0.6359649125 Combine like terms: 3.634758439 + 0.6359649125 = 4.2707233515 x = 4.2707233515 Simplifying x = 4.2707233515Subproblem 2
x + -0.6359649125 = -3.634758439 Simplifying x + -0.6359649125 = -3.634758439 Reorder the terms: -0.6359649125 + x = -3.634758439 Solving -0.6359649125 + x = -3.634758439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6359649125' to each side of the equation. -0.6359649125 + 0.6359649125 + x = -3.634758439 + 0.6359649125 Combine like terms: -0.6359649125 + 0.6359649125 = 0.0000000000 0.0000000000 + x = -3.634758439 + 0.6359649125 x = -3.634758439 + 0.6359649125 Combine like terms: -3.634758439 + 0.6359649125 = -2.9987935265 x = -2.9987935265 Simplifying x = -2.9987935265Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2707233515, -2.9987935265}
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