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Simplifying x2 + 9x + 14x + 14 = 180 Reorder the terms: 14 + 9x + 14x + x2 = 180 Combine like terms: 9x + 14x = 23x 14 + 23x + x2 = 180 Solving 14 + 23x + x2 = 180 Solving for variable 'x'. Reorder the terms: 14 + -180 + 23x + x2 = 180 + -180 Combine like terms: 14 + -180 = -166 -166 + 23x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -166 + 23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + 23x + 166 + x2 = 0 + 166 Reorder the terms: -166 + 166 + 23x + x2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + 23x + x2 = 0 + 166 23x + x2 = 0 + 166 Combine like terms: 0 + 166 = 166 23x + x2 = 166 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 166 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 166 + 132.25 Combine like terms: 166 + 132.25 = 298.25 132.25 + 23x + x2 = 298.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 298.25 Calculate the square root of the right side: 17.269916039 Break this problem into two subproblems by setting (x + 11.5) equal to 17.269916039 and -17.269916039.Subproblem 1
x + 11.5 = 17.269916039 Simplifying x + 11.5 = 17.269916039 Reorder the terms: 11.5 + x = 17.269916039 Solving 11.5 + x = 17.269916039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 17.269916039 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 17.269916039 + -11.5 x = 17.269916039 + -11.5 Combine like terms: 17.269916039 + -11.5 = 5.769916039 x = 5.769916039 Simplifying x = 5.769916039Subproblem 2
x + 11.5 = -17.269916039 Simplifying x + 11.5 = -17.269916039 Reorder the terms: 11.5 + x = -17.269916039 Solving 11.5 + x = -17.269916039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -17.269916039 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -17.269916039 + -11.5 x = -17.269916039 + -11.5 Combine like terms: -17.269916039 + -11.5 = -28.769916039 x = -28.769916039 Simplifying x = -28.769916039Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.769916039, -28.769916039}
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