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Simplifying 5 + 0.1x + 0.0003x2 = 59 Solving 5 + 0.1x + 0.0003x2 = 59 Solving for variable 'x'. Reorder the terms: 5 + -59 + 0.1x + 0.0003x2 = 59 + -59 Combine like terms: 5 + -59 = -54 -54 + 0.1x + 0.0003x2 = 59 + -59 Combine like terms: 59 + -59 = 0 -54 + 0.1x + 0.0003x2 = 0 Begin completing the square. Divide all terms by 0.0003 the coefficient of the squared term: Divide each side by '0.0003'. -180000 + 333.3333333x + x2 = 0 Move the constant term to the right: Add '180000' to each side of the equation. -180000 + 333.3333333x + 180000 + x2 = 0 + 180000 Reorder the terms: -180000 + 180000 + 333.3333333x + x2 = 0 + 180000 Combine like terms: -180000 + 180000 = 0 0 + 333.3333333x + x2 = 0 + 180000 333.3333333x + x2 = 0 + 180000 Combine like terms: 0 + 180000 = 180000 333.3333333x + x2 = 180000 The x term is 333.3333333x. Take half its coefficient (166.6666667). Square it (27777.77779) and add it to both sides. Add '27777.77779' to each side of the equation. 333.3333333x + 27777.77779 + x2 = 180000 + 27777.77779 Reorder the terms: 27777.77779 + 333.3333333x + x2 = 180000 + 27777.77779 Combine like terms: 180000 + 27777.77779 = 207777.77779 27777.77779 + 333.3333333x + x2 = 207777.77779 Factor a perfect square on the left side: (x + 166.6666667)(x + 166.6666667) = 207777.77779 Calculate the square root of the right side: 455.826477719 Break this problem into two subproblems by setting (x + 166.6666667) equal to 455.826477719 and -455.826477719.Subproblem 1
x + 166.6666667 = 455.826477719 Simplifying x + 166.6666667 = 455.826477719 Reorder the terms: 166.6666667 + x = 455.826477719 Solving 166.6666667 + x = 455.826477719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-166.6666667' to each side of the equation. 166.6666667 + -166.6666667 + x = 455.826477719 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = 455.826477719 + -166.6666667 x = 455.826477719 + -166.6666667 Combine like terms: 455.826477719 + -166.6666667 = 289.159811019 x = 289.159811019 Simplifying x = 289.159811019Subproblem 2
x + 166.6666667 = -455.826477719 Simplifying x + 166.6666667 = -455.826477719 Reorder the terms: 166.6666667 + x = -455.826477719 Solving 166.6666667 + x = -455.826477719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-166.6666667' to each side of the equation. 166.6666667 + -166.6666667 + x = -455.826477719 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = -455.826477719 + -166.6666667 x = -455.826477719 + -166.6666667 Combine like terms: -455.826477719 + -166.6666667 = -622.493144419 x = -622.493144419 Simplifying x = -622.493144419Solution
The solution to the problem is based on the solutions from the subproblems. x = {289.159811019, -622.493144419}
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