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Simplifying 0.006x2 + 0.2x + -50 = 50 Reorder the terms: -50 + 0.2x + 0.006x2 = 50 Solving -50 + 0.2x + 0.006x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -50 + 0.2x + 0.006x2 = 50 + -50 Combine like terms: -50 + -50 = -100 -100 + 0.2x + 0.006x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -100 + 0.2x + 0.006x2 = 0 Begin completing the square. Divide all terms by 0.006 the coefficient of the squared term: Divide each side by '0.006'. -16666.66667 + 33.33333333x + x2 = 0 Move the constant term to the right: Add '16666.66667' to each side of the equation. -16666.66667 + 33.33333333x + 16666.66667 + x2 = 0 + 16666.66667 Reorder the terms: -16666.66667 + 16666.66667 + 33.33333333x + x2 = 0 + 16666.66667 Combine like terms: -16666.66667 + 16666.66667 = 0.00000 0.00000 + 33.33333333x + x2 = 0 + 16666.66667 33.33333333x + x2 = 0 + 16666.66667 Combine like terms: 0 + 16666.66667 = 16666.66667 33.33333333x + x2 = 16666.66667 The x term is 33.33333333x. Take half its coefficient (16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. 33.33333333x + 277.7777779 + x2 = 16666.66667 + 277.7777779 Reorder the terms: 277.7777779 + 33.33333333x + x2 = 16666.66667 + 277.7777779 Combine like terms: 16666.66667 + 277.7777779 = 16944.4444479 277.7777779 + 33.33333333x + x2 = 16944.4444479 Factor a perfect square on the left side: (x + 16.66666667)(x + 16.66666667) = 16944.4444479 Calculate the square root of the right side: 130.170827945 Break this problem into two subproblems by setting (x + 16.66666667) equal to 130.170827945 and -130.170827945.Subproblem 1
x + 16.66666667 = 130.170827945 Simplifying x + 16.66666667 = 130.170827945 Reorder the terms: 16.66666667 + x = 130.170827945 Solving 16.66666667 + x = 130.170827945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + x = 130.170827945 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = 130.170827945 + -16.66666667 x = 130.170827945 + -16.66666667 Combine like terms: 130.170827945 + -16.66666667 = 113.504161275 x = 113.504161275 Simplifying x = 113.504161275Subproblem 2
x + 16.66666667 = -130.170827945 Simplifying x + 16.66666667 = -130.170827945 Reorder the terms: 16.66666667 + x = -130.170827945 Solving 16.66666667 + x = -130.170827945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + x = -130.170827945 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + x = -130.170827945 + -16.66666667 x = -130.170827945 + -16.66666667 Combine like terms: -130.170827945 + -16.66666667 = -146.837494615 x = -146.837494615 Simplifying x = -146.837494615Solution
The solution to the problem is based on the solutions from the subproblems. x = {113.504161275, -146.837494615}
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