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Simplifying 15o2 + 36o + 17 = 0 Reorder the terms: 17 + 36o + 15o2 = 0 Solving 17 + 36o + 15o2 = 0 Solving for variable 'o'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.133333333 + 2.4o + o2 = 0 Move the constant term to the right: Add '-1.133333333' to each side of the equation. 1.133333333 + 2.4o + -1.133333333 + o2 = 0 + -1.133333333 Reorder the terms: 1.133333333 + -1.133333333 + 2.4o + o2 = 0 + -1.133333333 Combine like terms: 1.133333333 + -1.133333333 = 0.000000000 0.000000000 + 2.4o + o2 = 0 + -1.133333333 2.4o + o2 = 0 + -1.133333333 Combine like terms: 0 + -1.133333333 = -1.133333333 2.4o + o2 = -1.133333333 The o term is 2.4o. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4o + 1.44 + o2 = -1.133333333 + 1.44 Reorder the terms: 1.44 + 2.4o + o2 = -1.133333333 + 1.44 Combine like terms: -1.133333333 + 1.44 = 0.306666667 1.44 + 2.4o + o2 = 0.306666667 Factor a perfect square on the left side: (o + 1.2)(o + 1.2) = 0.306666667 Calculate the square root of the right side: 0.553774924 Break this problem into two subproblems by setting (o + 1.2) equal to 0.553774924 and -0.553774924.Subproblem 1
o + 1.2 = 0.553774924 Simplifying o + 1.2 = 0.553774924 Reorder the terms: 1.2 + o = 0.553774924 Solving 1.2 + o = 0.553774924 Solving for variable 'o'. Move all terms containing o to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + o = 0.553774924 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + o = 0.553774924 + -1.2 o = 0.553774924 + -1.2 Combine like terms: 0.553774924 + -1.2 = -0.646225076 o = -0.646225076 Simplifying o = -0.646225076Subproblem 2
o + 1.2 = -0.553774924 Simplifying o + 1.2 = -0.553774924 Reorder the terms: 1.2 + o = -0.553774924 Solving 1.2 + o = -0.553774924 Solving for variable 'o'. Move all terms containing o to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + o = -0.553774924 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + o = -0.553774924 + -1.2 o = -0.553774924 + -1.2 Combine like terms: -0.553774924 + -1.2 = -1.753774924 o = -1.753774924 Simplifying o = -1.753774924Solution
The solution to the problem is based on the solutions from the subproblems. o = {-0.646225076, -1.753774924}
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