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Simplifying 0.0002x2 + -0.316x + -127.9 = 4 Reorder the terms: -127.9 + -0.316x + 0.0002x2 = 4 Solving -127.9 + -0.316x + 0.0002x2 = 4 Solving for variable 'x'. Reorder the terms: -127.9 + -4 + -0.316x + 0.0002x2 = 4 + -4 Combine like terms: -127.9 + -4 = -131.9 -131.9 + -0.316x + 0.0002x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -131.9 + -0.316x + 0.0002x2 = 0 Begin completing the square. Divide all terms by 0.0002 the coefficient of the squared term: Divide each side by '0.0002'. -659500 + -1580x + x2 = 0 Move the constant term to the right: Add '659500' to each side of the equation. -659500 + -1580x + 659500 + x2 = 0 + 659500 Reorder the terms: -659500 + 659500 + -1580x + x2 = 0 + 659500 Combine like terms: -659500 + 659500 = 0 0 + -1580x + x2 = 0 + 659500 -1580x + x2 = 0 + 659500 Combine like terms: 0 + 659500 = 659500 -1580x + x2 = 659500 The x term is -1580x. Take half its coefficient (-790). Square it (624100) and add it to both sides. Add '624100' to each side of the equation. -1580x + 624100 + x2 = 659500 + 624100 Reorder the terms: 624100 + -1580x + x2 = 659500 + 624100 Combine like terms: 659500 + 624100 = 1283600 624100 + -1580x + x2 = 1283600 Factor a perfect square on the left side: (x + -790)(x + -790) = 1283600 Calculate the square root of the right side: 1132.960723061 Break this problem into two subproblems by setting (x + -790) equal to 1132.960723061 and -1132.960723061.Subproblem 1
x + -790 = 1132.960723061 Simplifying x + -790 = 1132.960723061 Reorder the terms: -790 + x = 1132.960723061 Solving -790 + x = 1132.960723061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = 1132.960723061 + 790 Combine like terms: -790 + 790 = 0 0 + x = 1132.960723061 + 790 x = 1132.960723061 + 790 Combine like terms: 1132.960723061 + 790 = 1922.960723061 x = 1922.960723061 Simplifying x = 1922.960723061Subproblem 2
x + -790 = -1132.960723061 Simplifying x + -790 = -1132.960723061 Reorder the terms: -790 + x = -1132.960723061 Solving -790 + x = -1132.960723061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = -1132.960723061 + 790 Combine like terms: -790 + 790 = 0 0 + x = -1132.960723061 + 790 x = -1132.960723061 + 790 Combine like terms: -1132.960723061 + 790 = -342.960723061 x = -342.960723061 Simplifying x = -342.960723061Solution
The solution to the problem is based on the solutions from the subproblems. x = {1922.960723061, -342.960723061}
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