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Simplifying 0.0003x2 + 0.1x + 10 = 67 Reorder the terms: 10 + 0.1x + 0.0003x2 = 67 Solving 10 + 0.1x + 0.0003x2 = 67 Solving for variable 'x'. Reorder the terms: 10 + -67 + 0.1x + 0.0003x2 = 67 + -67 Combine like terms: 10 + -67 = -57 -57 + 0.1x + 0.0003x2 = 67 + -67 Combine like terms: 67 + -67 = 0 -57 + 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'. -190000 + 333.3333333x + x2 = 0 Move the constant term to the right: Add '190000' to each side of the equation. -190000 + 333.3333333x + 190000 + x2 = 0 + 190000 Reorder the terms: -190000 + 190000 + 333.3333333x + x2 = 0 + 190000 Combine like terms: -190000 + 190000 = 0 0 + 333.3333333x + x2 = 0 + 190000 333.3333333x + x2 = 0 + 190000 Combine like terms: 0 + 190000 = 190000 333.3333333x + x2 = 190000 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 = 190000 + 27777.77779 Reorder the terms: 27777.77779 + 333.3333333x + x2 = 190000 + 27777.77779 Combine like terms: 190000 + 27777.77779 = 217777.77779 27777.77779 + 333.3333333x + x2 = 217777.77779 Factor a perfect square on the left side: (x + 166.6666667)(x + 166.6666667) = 217777.77779 Calculate the square root of the right side: 466.66666668 Break this problem into two subproblems by setting (x + 166.6666667) equal to 466.66666668 and -466.66666668.Subproblem 1
x + 166.6666667 = 466.66666668 Simplifying x + 166.6666667 = 466.66666668 Reorder the terms: 166.6666667 + x = 466.66666668 Solving 166.6666667 + x = 466.66666668 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 = 466.66666668 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = 466.66666668 + -166.6666667 x = 466.66666668 + -166.6666667 Combine like terms: 466.66666668 + -166.6666667 = 299.99999998 x = 299.99999998 Simplifying x = 299.99999998Subproblem 2
x + 166.6666667 = -466.66666668 Simplifying x + 166.6666667 = -466.66666668 Reorder the terms: 166.6666667 + x = -466.66666668 Solving 166.6666667 + x = -466.66666668 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 = -466.66666668 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + x = -466.66666668 + -166.6666667 x = -466.66666668 + -166.6666667 Combine like terms: -466.66666668 + -166.6666667 = -633.33333338 x = -633.33333338 Simplifying x = -633.33333338Solution
The solution to the problem is based on the solutions from the subproblems. x = {299.99999998, -633.33333338}
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