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Simplifying 67 = 0.0003x2 + 0.1x + 20 Reorder the terms: 67 = 20 + 0.1x + 0.0003x2 Solving 67 = 20 + 0.1x + 0.0003x2 Solving for variable 'x'. Combine like terms: 67 + -20 = 47 47 + -0.1x + -0.0003x2 = 20 + 0.1x + 0.0003x2 + -20 + -0.1x + -0.0003x2 Reorder the terms: 47 + -0.1x + -0.0003x2 = 20 + -20 + 0.1x + -0.1x + 0.0003x2 + -0.0003x2 Combine like terms: 20 + -20 = 0 47 + -0.1x + -0.0003x2 = 0 + 0.1x + -0.1x + 0.0003x2 + -0.0003x2 47 + -0.1x + -0.0003x2 = 0.1x + -0.1x + 0.0003x2 + -0.0003x2 Combine like terms: 0.1x + -0.1x = 0.0 47 + -0.1x + -0.0003x2 = 0.0 + 0.0003x2 + -0.0003x2 47 + -0.1x + -0.0003x2 = 0.0003x2 + -0.0003x2 Combine like terms: 0.0003x2 + -0.0003x2 = 0.0000 47 + -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'. -156666.6667 + 333.3333333x + x2 = 0 Move the constant term to the right: Add '156666.6667' to each side of the equation. -156666.6667 + 333.3333333x + 156666.6667 + x2 = 0 + 156666.6667 Reorder the terms: -156666.6667 + 156666.6667 + 333.3333333x + x2 = 0 + 156666.6667 Combine like terms: -156666.6667 + 156666.6667 = 0.0000 0.0000 + 333.3333333x + x2 = 0 + 156666.6667 333.3333333x + x2 = 0 + 156666.6667 Combine like terms: 0 + 156666.6667 = 156666.6667 333.3333333x + x2 = 156666.6667 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 = 156666.6667 + 27777.77779 Reorder the terms: 27777.77779 + 333.3333333x + x2 = 156666.6667 + 27777.77779 Combine like terms: 156666.6667 + 27777.77779 = 184444.44449 27777.77779 + 333.3333333x + x2 = 184444.44449 Factor a perfect square on the left side: (x + 166.6666667)(x + 166.6666667) = 184444.44449 Calculate the square root of the right side: 429.469957611 Break this problem into two subproblems by setting (x + 166.6666667) equal to 429.469957611 and -429.469957611.Subproblem 1
x + 166.6666667 = 429.469957611 Simplifying x + 166.6666667 = 429.469957611 Reorder the terms: 166.6666667 + x = 429.469957611 Solving 166.6666667 + x = 429.469957611 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 = 429.469957611 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = 429.469957611 + -166.6666667 x = 429.469957611 + -166.6666667 Combine like terms: 429.469957611 + -166.6666667 = 262.803290911 x = 262.803290911 Simplifying x = 262.803290911Subproblem 2
x + 166.6666667 = -429.469957611 Simplifying x + 166.6666667 = -429.469957611 Reorder the terms: 166.6666667 + x = -429.469957611 Solving 166.6666667 + x = -429.469957611 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 = -429.469957611 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = -429.469957611 + -166.6666667 x = -429.469957611 + -166.6666667 Combine like terms: -429.469957611 + -166.6666667 = -596.136624311 x = -596.136624311 Simplifying x = -596.136624311Solution
The solution to the problem is based on the solutions from the subproblems. x = {262.803290911, -596.136624311}
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