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Simplifying 2.2X2 + 7.6X + 1.4 = 0 Reorder the terms: 1.4 + 7.6X + 2.2X2 = 0 Solving 1.4 + 7.6X + 2.2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2.2 the coefficient of the squared term: Divide each side by '2.2'. 0.6363636364 + 3.454545455X + X2 = 0 Move the constant term to the right: Add '-0.6363636364' to each side of the equation. 0.6363636364 + 3.454545455X + -0.6363636364 + X2 = 0 + -0.6363636364 Reorder the terms: 0.6363636364 + -0.6363636364 + 3.454545455X + X2 = 0 + -0.6363636364 Combine like terms: 0.6363636364 + -0.6363636364 = 0.0000000000 0.0000000000 + 3.454545455X + X2 = 0 + -0.6363636364 3.454545455X + X2 = 0 + -0.6363636364 Combine like terms: 0 + -0.6363636364 = -0.6363636364 3.454545455X + X2 = -0.6363636364 The X term is 3.454545455X. Take half its coefficient (1.727272728). Square it (2.983471077) and add it to both sides. Add '2.983471077' to each side of the equation. 3.454545455X + 2.983471077 + X2 = -0.6363636364 + 2.983471077 Reorder the terms: 2.983471077 + 3.454545455X + X2 = -0.6363636364 + 2.983471077 Combine like terms: -0.6363636364 + 2.983471077 = 2.3471074406 2.983471077 + 3.454545455X + X2 = 2.3471074406 Factor a perfect square on the left side: (X + 1.727272728)(X + 1.727272728) = 2.3471074406 Calculate the square root of the right side: 1.532027232 Break this problem into two subproblems by setting (X + 1.727272728) equal to 1.532027232 and -1.532027232.Subproblem 1
X + 1.727272728 = 1.532027232 Simplifying X + 1.727272728 = 1.532027232 Reorder the terms: 1.727272728 + X = 1.532027232 Solving 1.727272728 + X = 1.532027232 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.727272728' to each side of the equation. 1.727272728 + -1.727272728 + X = 1.532027232 + -1.727272728 Combine like terms: 1.727272728 + -1.727272728 = 0.000000000 0.000000000 + X = 1.532027232 + -1.727272728 X = 1.532027232 + -1.727272728 Combine like terms: 1.532027232 + -1.727272728 = -0.195245496 X = -0.195245496 Simplifying X = -0.195245496Subproblem 2
X + 1.727272728 = -1.532027232 Simplifying X + 1.727272728 = -1.532027232 Reorder the terms: 1.727272728 + X = -1.532027232 Solving 1.727272728 + X = -1.532027232 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.727272728' to each side of the equation. 1.727272728 + -1.727272728 + X = -1.532027232 + -1.727272728 Combine like terms: 1.727272728 + -1.727272728 = 0.000000000 0.000000000 + X = -1.532027232 + -1.727272728 X = -1.532027232 + -1.727272728 Combine like terms: -1.532027232 + -1.727272728 = -3.25929996 X = -3.25929996 Simplifying X = -3.25929996Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.195245496, -3.25929996}
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