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Simplifying 55 = 15 + 0.1x + 0.0003x2 Solving 55 = 15 + 0.1x + 0.0003x2 Solving for variable 'x'. Combine like terms: 55 + -15 = 40 40 + -0.1x + -0.0003x2 = 15 + 0.1x + 0.0003x2 + -15 + -0.1x + -0.0003x2 Reorder the terms: 40 + -0.1x + -0.0003x2 = 15 + -15 + 0.1x + -0.1x + 0.0003x2 + -0.0003x2 Combine like terms: 15 + -15 = 0 40 + -0.1x + -0.0003x2 = 0 + 0.1x + -0.1x + 0.0003x2 + -0.0003x2 40 + -0.1x + -0.0003x2 = 0.1x + -0.1x + 0.0003x2 + -0.0003x2 Combine like terms: 0.1x + -0.1x = 0.0 40 + -0.1x + -0.0003x2 = 0.0 + 0.0003x2 + -0.0003x2 40 + -0.1x + -0.0003x2 = 0.0003x2 + -0.0003x2 Combine like terms: 0.0003x2 + -0.0003x2 = 0.0000 40 + -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'. -133333.3333 + 333.3333333x + x2 = 0 Move the constant term to the right: Add '133333.3333' to each side of the equation. -133333.3333 + 333.3333333x + 133333.3333 + x2 = 0 + 133333.3333 Reorder the terms: -133333.3333 + 133333.3333 + 333.3333333x + x2 = 0 + 133333.3333 Combine like terms: -133333.3333 + 133333.3333 = 0.0000 0.0000 + 333.3333333x + x2 = 0 + 133333.3333 333.3333333x + x2 = 0 + 133333.3333 Combine like terms: 0 + 133333.3333 = 133333.3333 333.3333333x + x2 = 133333.3333 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 = 133333.3333 + 27777.77779 Reorder the terms: 27777.77779 + 333.3333333x + x2 = 133333.3333 + 27777.77779 Combine like terms: 133333.3333 + 27777.77779 = 161111.11109 27777.77779 + 333.3333333x + x2 = 161111.11109 Factor a perfect square on the left side: (x + 166.6666667)(x + 166.6666667) = 161111.11109 Calculate the square root of the right side: 401.386485933 Break this problem into two subproblems by setting (x + 166.6666667) equal to 401.386485933 and -401.386485933.Subproblem 1
x + 166.6666667 = 401.386485933 Simplifying x + 166.6666667 = 401.386485933 Reorder the terms: 166.6666667 + x = 401.386485933 Solving 166.6666667 + x = 401.386485933 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 = 401.386485933 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = 401.386485933 + -166.6666667 x = 401.386485933 + -166.6666667 Combine like terms: 401.386485933 + -166.6666667 = 234.719819233 x = 234.719819233 Simplifying x = 234.719819233Subproblem 2
x + 166.6666667 = -401.386485933 Simplifying x + 166.6666667 = -401.386485933 Reorder the terms: 166.6666667 + x = -401.386485933 Solving 166.6666667 + x = -401.386485933 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 = -401.386485933 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = -401.386485933 + -166.6666667 x = -401.386485933 + -166.6666667 Combine like terms: -401.386485933 + -166.6666667 = -568.053152633 x = -568.053152633 Simplifying x = -568.053152633Solution
The solution to the problem is based on the solutions from the subproblems. x = {234.719819233, -568.053152633}
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