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Simplifying 0.199x2 + -0.009x + -0.452 = 0 Reorder the terms: -0.452 + -0.009x + 0.199x2 = 0 Solving -0.452 + -0.009x + 0.199x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.199 the coefficient of the squared term: Divide each side by '0.199'. -2.271356784 + -0.04522613065x + x2 = 0 Move the constant term to the right: Add '2.271356784' to each side of the equation. -2.271356784 + -0.04522613065x + 2.271356784 + x2 = 0 + 2.271356784 Reorder the terms: -2.271356784 + 2.271356784 + -0.04522613065x + x2 = 0 + 2.271356784 Combine like terms: -2.271356784 + 2.271356784 = 0.000000000 0.000000000 + -0.04522613065x + x2 = 0 + 2.271356784 -0.04522613065x + x2 = 0 + 2.271356784 Combine like terms: 0 + 2.271356784 = 2.271356784 -0.04522613065x + x2 = 2.271356784 The x term is -0.04522613065x. Take half its coefficient (-0.02261306533). Square it (0.0005113507236) and add it to both sides. Add '0.0005113507236' to each side of the equation. -0.04522613065x + 0.0005113507236 + x2 = 2.271356784 + 0.0005113507236 Reorder the terms: 0.0005113507236 + -0.04522613065x + x2 = 2.271356784 + 0.0005113507236 Combine like terms: 2.271356784 + 0.0005113507236 = 2.2718681347236 0.0005113507236 + -0.04522613065x + x2 = 2.2718681347236 Factor a perfect square on the left side: (x + -0.02261306533)(x + -0.02261306533) = 2.2718681347236 Calculate the square root of the right side: 1.507271752 Break this problem into two subproblems by setting (x + -0.02261306533) equal to 1.507271752 and -1.507271752.Subproblem 1
x + -0.02261306533 = 1.507271752 Simplifying x + -0.02261306533 = 1.507271752 Reorder the terms: -0.02261306533 + x = 1.507271752 Solving -0.02261306533 + x = 1.507271752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02261306533' to each side of the equation. -0.02261306533 + 0.02261306533 + x = 1.507271752 + 0.02261306533 Combine like terms: -0.02261306533 + 0.02261306533 = 0.00000000000 0.00000000000 + x = 1.507271752 + 0.02261306533 x = 1.507271752 + 0.02261306533 Combine like terms: 1.507271752 + 0.02261306533 = 1.52988481733 x = 1.52988481733 Simplifying x = 1.52988481733Subproblem 2
x + -0.02261306533 = -1.507271752 Simplifying x + -0.02261306533 = -1.507271752 Reorder the terms: -0.02261306533 + x = -1.507271752 Solving -0.02261306533 + x = -1.507271752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02261306533' to each side of the equation. -0.02261306533 + 0.02261306533 + x = -1.507271752 + 0.02261306533 Combine like terms: -0.02261306533 + 0.02261306533 = 0.00000000000 0.00000000000 + x = -1.507271752 + 0.02261306533 x = -1.507271752 + 0.02261306533 Combine like terms: -1.507271752 + 0.02261306533 = -1.48465868667 x = -1.48465868667 Simplifying x = -1.48465868667Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.52988481733, -1.48465868667}
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