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Simplifying 3.142x2 + -1x + -26(3.142) = 0 Multiply -26 * 3.142 3.142x2 + -1x + -81.692 = 0 Reorder the terms: -81.692 + -1x + 3.142x2 = 0 Solving -81.692 + -1x + 3.142x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.142 the coefficient of the squared term: Divide each side by '3.142'. -26 + -0.3182686187x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -0.3182686187x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -0.3182686187x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -0.3182686187x + x2 = 0 + 26 -0.3182686187x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -0.3182686187x + x2 = 26 The x term is -0.3182686187x. Take half its coefficient (-0.1591343094). Square it (0.02532372843) and add it to both sides. Add '0.02532372843' to each side of the equation. -0.3182686187x + 0.02532372843 + x2 = 26 + 0.02532372843 Reorder the terms: 0.02532372843 + -0.3182686187x + x2 = 26 + 0.02532372843 Combine like terms: 26 + 0.02532372843 = 26.02532372843 0.02532372843 + -0.3182686187x + x2 = 26.02532372843 Factor a perfect square on the left side: (x + -0.1591343094)(x + -0.1591343094) = 26.02532372843 Calculate the square root of the right side: 5.101502105 Break this problem into two subproblems by setting (x + -0.1591343094) equal to 5.101502105 and -5.101502105.Subproblem 1
x + -0.1591343094 = 5.101502105 Simplifying x + -0.1591343094 = 5.101502105 Reorder the terms: -0.1591343094 + x = 5.101502105 Solving -0.1591343094 + x = 5.101502105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1591343094' to each side of the equation. -0.1591343094 + 0.1591343094 + x = 5.101502105 + 0.1591343094 Combine like terms: -0.1591343094 + 0.1591343094 = 0.0000000000 0.0000000000 + x = 5.101502105 + 0.1591343094 x = 5.101502105 + 0.1591343094 Combine like terms: 5.101502105 + 0.1591343094 = 5.2606364144 x = 5.2606364144 Simplifying x = 5.2606364144Subproblem 2
x + -0.1591343094 = -5.101502105 Simplifying x + -0.1591343094 = -5.101502105 Reorder the terms: -0.1591343094 + x = -5.101502105 Solving -0.1591343094 + x = -5.101502105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1591343094' to each side of the equation. -0.1591343094 + 0.1591343094 + x = -5.101502105 + 0.1591343094 Combine like terms: -0.1591343094 + 0.1591343094 = 0.0000000000 0.0000000000 + x = -5.101502105 + 0.1591343094 x = -5.101502105 + 0.1591343094 Combine like terms: -5.101502105 + 0.1591343094 = -4.9423677956 x = -4.9423677956 Simplifying x = -4.9423677956Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2606364144, -4.9423677956}
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