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Simplifying 2.7384 + 2.608x + -165x2 = 0 Solving 2.7384 + 2.608x + -165x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -165 the coefficient of the squared term: Divide each side by '-165'. -0.01659636364 + -0.01580606061x + x2 = 0 Move the constant term to the right: Add '0.01659636364' to each side of the equation. -0.01659636364 + -0.01580606061x + 0.01659636364 + x2 = 0 + 0.01659636364 Reorder the terms: -0.01659636364 + 0.01659636364 + -0.01580606061x + x2 = 0 + 0.01659636364 Combine like terms: -0.01659636364 + 0.01659636364 = 0.00000000000 0.00000000000 + -0.01580606061x + x2 = 0 + 0.01659636364 -0.01580606061x + x2 = 0 + 0.01659636364 Combine like terms: 0 + 0.01659636364 = 0.01659636364 -0.01580606061x + x2 = 0.01659636364 The x term is -0.01580606061x. Take half its coefficient (-0.007903030305). Square it (0.00006245788800) and add it to both sides. Add '0.00006245788800' to each side of the equation. -0.01580606061x + 0.00006245788800 + x2 = 0.01659636364 + 0.00006245788800 Reorder the terms: 0.00006245788800 + -0.01580606061x + x2 = 0.01659636364 + 0.00006245788800 Combine like terms: 0.01659636364 + 0.00006245788800 = 0.016658821528 0.00006245788800 + -0.01580606061x + x2 = 0.016658821528 Factor a perfect square on the left side: (x + -0.007903030305)(x + -0.007903030305) = 0.016658821528 Calculate the square root of the right side: 0.129069057 Break this problem into two subproblems by setting (x + -0.007903030305) equal to 0.129069057 and -0.129069057.Subproblem 1
x + -0.007903030305 = 0.129069057 Simplifying x + -0.007903030305 = 0.129069057 Reorder the terms: -0.007903030305 + x = 0.129069057 Solving -0.007903030305 + x = 0.129069057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.007903030305' to each side of the equation. -0.007903030305 + 0.007903030305 + x = 0.129069057 + 0.007903030305 Combine like terms: -0.007903030305 + 0.007903030305 = 0.000000000000 0.000000000000 + x = 0.129069057 + 0.007903030305 x = 0.129069057 + 0.007903030305 Combine like terms: 0.129069057 + 0.007903030305 = 0.136972087305 x = 0.136972087305 Simplifying x = 0.136972087305Subproblem 2
x + -0.007903030305 = -0.129069057 Simplifying x + -0.007903030305 = -0.129069057 Reorder the terms: -0.007903030305 + x = -0.129069057 Solving -0.007903030305 + x = -0.129069057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.007903030305' to each side of the equation. -0.007903030305 + 0.007903030305 + x = -0.129069057 + 0.007903030305 Combine like terms: -0.007903030305 + 0.007903030305 = 0.000000000000 0.000000000000 + x = -0.129069057 + 0.007903030305 x = -0.129069057 + 0.007903030305 Combine like terms: -0.129069057 + 0.007903030305 = -0.121166026695 x = -0.121166026695 Simplifying x = -0.121166026695Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.136972087305, -0.121166026695}
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