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Simplifying 0.645x2 + -11.844x + 21.056 = 0 Reorder the terms: 21.056 + -11.844x + 0.645x2 = 0 Solving 21.056 + -11.844x + 0.645x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.645 the coefficient of the squared term: Divide each side by '0.645'. 32.64496124 + -18.3627907x + x2 = 0 Move the constant term to the right: Add '-32.64496124' to each side of the equation. 32.64496124 + -18.3627907x + -32.64496124 + x2 = 0 + -32.64496124 Reorder the terms: 32.64496124 + -32.64496124 + -18.3627907x + x2 = 0 + -32.64496124 Combine like terms: 32.64496124 + -32.64496124 = 0.00000000 0.00000000 + -18.3627907x + x2 = 0 + -32.64496124 -18.3627907x + x2 = 0 + -32.64496124 Combine like terms: 0 + -32.64496124 = -32.64496124 -18.3627907x + x2 = -32.64496124 The x term is -18.3627907x. Take half its coefficient (-9.18139535). Square it (84.29802057) and add it to both sides. Add '84.29802057' to each side of the equation. -18.3627907x + 84.29802057 + x2 = -32.64496124 + 84.29802057 Reorder the terms: 84.29802057 + -18.3627907x + x2 = -32.64496124 + 84.29802057 Combine like terms: -32.64496124 + 84.29802057 = 51.65305933 84.29802057 + -18.3627907x + x2 = 51.65305933 Factor a perfect square on the left side: (x + -9.18139535)(x + -9.18139535) = 51.65305933 Calculate the square root of the right side: 7.187006284 Break this problem into two subproblems by setting (x + -9.18139535) equal to 7.187006284 and -7.187006284.Subproblem 1
x + -9.18139535 = 7.187006284 Simplifying x + -9.18139535 = 7.187006284 Reorder the terms: -9.18139535 + x = 7.187006284 Solving -9.18139535 + x = 7.187006284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.18139535' to each side of the equation. -9.18139535 + 9.18139535 + x = 7.187006284 + 9.18139535 Combine like terms: -9.18139535 + 9.18139535 = 0.00000000 0.00000000 + x = 7.187006284 + 9.18139535 x = 7.187006284 + 9.18139535 Combine like terms: 7.187006284 + 9.18139535 = 16.368401634 x = 16.368401634 Simplifying x = 16.368401634Subproblem 2
x + -9.18139535 = -7.187006284 Simplifying x + -9.18139535 = -7.187006284 Reorder the terms: -9.18139535 + x = -7.187006284 Solving -9.18139535 + x = -7.187006284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.18139535' to each side of the equation. -9.18139535 + 9.18139535 + x = -7.187006284 + 9.18139535 Combine like terms: -9.18139535 + 9.18139535 = 0.00000000 0.00000000 + x = -7.187006284 + 9.18139535 x = -7.187006284 + 9.18139535 Combine like terms: -7.187006284 + 9.18139535 = 1.994389066 x = 1.994389066 Simplifying x = 1.994389066Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.368401634, 1.994389066}
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