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Simplifying 67 = 15 + 0.1x + 0.0003x2 Solving 67 = 15 + 0.1x + 0.0003x2 Solving for variable 'x'. Combine like terms: 67 + -15 = 52 52 + -0.1x + -0.0003x2 = 15 + 0.1x + 0.0003x2 + -15 + -0.1x + -0.0003x2 Reorder the terms: 52 + -0.1x + -0.0003x2 = 15 + -15 + 0.1x + -0.1x + 0.0003x2 + -0.0003x2 Combine like terms: 15 + -15 = 0 52 + -0.1x + -0.0003x2 = 0 + 0.1x + -0.1x + 0.0003x2 + -0.0003x2 52 + -0.1x + -0.0003x2 = 0.1x + -0.1x + 0.0003x2 + -0.0003x2 Combine like terms: 0.1x + -0.1x = 0.0 52 + -0.1x + -0.0003x2 = 0.0 + 0.0003x2 + -0.0003x2 52 + -0.1x + -0.0003x2 = 0.0003x2 + -0.0003x2 Combine like terms: 0.0003x2 + -0.0003x2 = 0.0000 52 + -0.1x + -0.0003x2 = 0.0000 Begin completing the square. Divide all terms by -0.0003 the coefficient of the squared term: Divide each side by '-0.0003'. -173333.3333 + 333.3333333x + x2 = 0 Move the constant term to the right: Add '173333.3333' to each side of the equation. -173333.3333 + 333.3333333x + 173333.3333 + x2 = 0 + 173333.3333 Reorder the terms: -173333.3333 + 173333.3333 + 333.3333333x + x2 = 0 + 173333.3333 Combine like terms: -173333.3333 + 173333.3333 = 0.0000 0.0000 + 333.3333333x + x2 = 0 + 173333.3333 333.3333333x + x2 = 0 + 173333.3333 Combine like terms: 0 + 173333.3333 = 173333.3333 333.3333333x + x2 = 173333.3333 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 = 173333.3333 + 27777.77779 Reorder the terms: 27777.77779 + 333.3333333x + x2 = 173333.3333 + 27777.77779 Combine like terms: 173333.3333 + 27777.77779 = 201111.11109 27777.77779 + 333.3333333x + x2 = 201111.11109 Factor a perfect square on the left side: (x + 166.6666667)(x + 166.6666667) = 201111.11109 Calculate the square root of the right side: 448.454134879 Break this problem into two subproblems by setting (x + 166.6666667) equal to 448.454134879 and -448.454134879.Subproblem 1
x + 166.6666667 = 448.454134879 Simplifying x + 166.6666667 = 448.454134879 Reorder the terms: 166.6666667 + x = 448.454134879 Solving 166.6666667 + x = 448.454134879 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 = 448.454134879 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = 448.454134879 + -166.6666667 x = 448.454134879 + -166.6666667 Combine like terms: 448.454134879 + -166.6666667 = 281.787468179 x = 281.787468179 Simplifying x = 281.787468179Subproblem 2
x + 166.6666667 = -448.454134879 Simplifying x + 166.6666667 = -448.454134879 Reorder the terms: 166.6666667 + x = -448.454134879 Solving 166.6666667 + x = -448.454134879 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 = -448.454134879 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = -448.454134879 + -166.6666667 x = -448.454134879 + -166.6666667 Combine like terms: -448.454134879 + -166.6666667 = -615.120801579 x = -615.120801579 Simplifying x = -615.120801579Solution
The solution to the problem is based on the solutions from the subproblems. x = {281.787468179, -615.120801579}
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