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Simplifying 36x2 + 31x + -15 = 0 Reorder the terms: -15 + 31x + 36x2 = 0 Solving -15 + 31x + 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'. -0.4166666667 + 0.8611111111x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.8611111111x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 0.8611111111x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 0.8611111111x + x2 = 0 + 0.4166666667 0.8611111111x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 0.8611111111x + x2 = 0.4166666667 The x term is 0.8611111111x. Take half its coefficient (0.4305555556). Square it (0.1853780865) and add it to both sides. Add '0.1853780865' to each side of the equation. 0.8611111111x + 0.1853780865 + x2 = 0.4166666667 + 0.1853780865 Reorder the terms: 0.1853780865 + 0.8611111111x + x2 = 0.4166666667 + 0.1853780865 Combine like terms: 0.4166666667 + 0.1853780865 = 0.6020447532 0.1853780865 + 0.8611111111x + x2 = 0.6020447532 Factor a perfect square on the left side: (x + 0.4305555556)(x + 0.4305555556) = 0.6020447532 Calculate the square root of the right side: 0.775915429 Break this problem into two subproblems by setting (x + 0.4305555556) equal to 0.775915429 and -0.775915429.Subproblem 1
x + 0.4305555556 = 0.775915429 Simplifying x + 0.4305555556 = 0.775915429 Reorder the terms: 0.4305555556 + x = 0.775915429 Solving 0.4305555556 + x = 0.775915429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4305555556' to each side of the equation. 0.4305555556 + -0.4305555556 + x = 0.775915429 + -0.4305555556 Combine like terms: 0.4305555556 + -0.4305555556 = 0.0000000000 0.0000000000 + x = 0.775915429 + -0.4305555556 x = 0.775915429 + -0.4305555556 Combine like terms: 0.775915429 + -0.4305555556 = 0.3453598734 x = 0.3453598734 Simplifying x = 0.3453598734Subproblem 2
x + 0.4305555556 = -0.775915429 Simplifying x + 0.4305555556 = -0.775915429 Reorder the terms: 0.4305555556 + x = -0.775915429 Solving 0.4305555556 + x = -0.775915429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4305555556' to each side of the equation. 0.4305555556 + -0.4305555556 + x = -0.775915429 + -0.4305555556 Combine like terms: 0.4305555556 + -0.4305555556 = 0.0000000000 0.0000000000 + x = -0.775915429 + -0.4305555556 x = -0.775915429 + -0.4305555556 Combine like terms: -0.775915429 + -0.4305555556 = -1.2064709846 x = -1.2064709846 Simplifying x = -1.2064709846Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3453598734, -1.2064709846}
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