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Simplifying 36x2 + -85x + 6 = 0 Reorder the terms: 6 + -85x + 36x2 = 0 Solving 6 + -85x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.1666666667 + -2.361111111x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -2.361111111x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -2.361111111x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -2.361111111x + x2 = 0 + -0.1666666667 -2.361111111x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -2.361111111x + x2 = -0.1666666667 The x term is -2.361111111x. Take half its coefficient (-1.180555556). Square it (1.393711421) and add it to both sides. Add '1.393711421' to each side of the equation. -2.361111111x + 1.393711421 + x2 = -0.1666666667 + 1.393711421 Reorder the terms: 1.393711421 + -2.361111111x + x2 = -0.1666666667 + 1.393711421 Combine like terms: -0.1666666667 + 1.393711421 = 1.2270447543 1.393711421 + -2.361111111x + x2 = 1.2270447543 Factor a perfect square on the left side: (x + -1.180555556)(x + -1.180555556) = 1.2270447543 Calculate the square root of the right side: 1.107720522 Break this problem into two subproblems by setting (x + -1.180555556) equal to 1.107720522 and -1.107720522.Subproblem 1
x + -1.180555556 = 1.107720522 Simplifying x + -1.180555556 = 1.107720522 Reorder the terms: -1.180555556 + x = 1.107720522 Solving -1.180555556 + x = 1.107720522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.180555556' to each side of the equation. -1.180555556 + 1.180555556 + x = 1.107720522 + 1.180555556 Combine like terms: -1.180555556 + 1.180555556 = 0.000000000 0.000000000 + x = 1.107720522 + 1.180555556 x = 1.107720522 + 1.180555556 Combine like terms: 1.107720522 + 1.180555556 = 2.288276078 x = 2.288276078 Simplifying x = 2.288276078Subproblem 2
x + -1.180555556 = -1.107720522 Simplifying x + -1.180555556 = -1.107720522 Reorder the terms: -1.180555556 + x = -1.107720522 Solving -1.180555556 + x = -1.107720522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.180555556' to each side of the equation. -1.180555556 + 1.180555556 + x = -1.107720522 + 1.180555556 Combine like terms: -1.180555556 + 1.180555556 = 0.000000000 0.000000000 + x = -1.107720522 + 1.180555556 x = -1.107720522 + 1.180555556 Combine like terms: -1.107720522 + 1.180555556 = 0.072835034 x = 0.072835034 Simplifying x = 0.072835034Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.288276078, 0.072835034}
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