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Simplifying 7.63x2 + 2.77x = 5.37 Reorder the terms: 2.77x + 7.63x2 = 5.37 Solving 2.77x + 7.63x2 = 5.37 Solving for variable 'x'. Reorder the terms: -5.37 + 2.77x + 7.63x2 = 5.37 + -5.37 Combine like terms: 5.37 + -5.37 = 0.00 -5.37 + 2.77x + 7.63x2 = 0.00 Begin completing the square. Divide all terms by 7.63 the coefficient of the squared term: Divide each side by '7.63'. -0.7038007864 + 0.3630406291x + x2 = 0 Move the constant term to the right: Add '0.7038007864' to each side of the equation. -0.7038007864 + 0.3630406291x + 0.7038007864 + x2 = 0 + 0.7038007864 Reorder the terms: -0.7038007864 + 0.7038007864 + 0.3630406291x + x2 = 0 + 0.7038007864 Combine like terms: -0.7038007864 + 0.7038007864 = 0.0000000000 0.0000000000 + 0.3630406291x + x2 = 0 + 0.7038007864 0.3630406291x + x2 = 0 + 0.7038007864 Combine like terms: 0 + 0.7038007864 = 0.7038007864 0.3630406291x + x2 = 0.7038007864 The x term is 0.3630406291x. Take half its coefficient (0.1815203146). Square it (0.03294962461) and add it to both sides. Add '0.03294962461' to each side of the equation. 0.3630406291x + 0.03294962461 + x2 = 0.7038007864 + 0.03294962461 Reorder the terms: 0.03294962461 + 0.3630406291x + x2 = 0.7038007864 + 0.03294962461 Combine like terms: 0.7038007864 + 0.03294962461 = 0.73675041101 0.03294962461 + 0.3630406291x + x2 = 0.73675041101 Factor a perfect square on the left side: (x + 0.1815203146)(x + 0.1815203146) = 0.73675041101 Calculate the square root of the right side: 0.858341663 Break this problem into two subproblems by setting (x + 0.1815203146) equal to 0.858341663 and -0.858341663.Subproblem 1
x + 0.1815203146 = 0.858341663 Simplifying x + 0.1815203146 = 0.858341663 Reorder the terms: 0.1815203146 + x = 0.858341663 Solving 0.1815203146 + x = 0.858341663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1815203146' to each side of the equation. 0.1815203146 + -0.1815203146 + x = 0.858341663 + -0.1815203146 Combine like terms: 0.1815203146 + -0.1815203146 = 0.0000000000 0.0000000000 + x = 0.858341663 + -0.1815203146 x = 0.858341663 + -0.1815203146 Combine like terms: 0.858341663 + -0.1815203146 = 0.6768213484 x = 0.6768213484 Simplifying x = 0.6768213484Subproblem 2
x + 0.1815203146 = -0.858341663 Simplifying x + 0.1815203146 = -0.858341663 Reorder the terms: 0.1815203146 + x = -0.858341663 Solving 0.1815203146 + x = -0.858341663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1815203146' to each side of the equation. 0.1815203146 + -0.1815203146 + x = -0.858341663 + -0.1815203146 Combine like terms: 0.1815203146 + -0.1815203146 = 0.0000000000 0.0000000000 + x = -0.858341663 + -0.1815203146 x = -0.858341663 + -0.1815203146 Combine like terms: -0.858341663 + -0.1815203146 = -1.0398619776 x = -1.0398619776 Simplifying x = -1.0398619776Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6768213484, -1.0398619776}
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