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Simplifying 0.0002x2 + -0.316x + 123.9 = 0 Reorder the terms: 123.9 + -0.316x + 0.0002x2 = 0 Solving 123.9 + -0.316x + 0.0002x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0002 the coefficient of the squared term: Divide each side by '0.0002'. 619500 + -1580x + x2 = 0 Move the constant term to the right: Add '-619500' to each side of the equation. 619500 + -1580x + -619500 + x2 = 0 + -619500 Reorder the terms: 619500 + -619500 + -1580x + x2 = 0 + -619500 Combine like terms: 619500 + -619500 = 0 0 + -1580x + x2 = 0 + -619500 -1580x + x2 = 0 + -619500 Combine like terms: 0 + -619500 = -619500 -1580x + x2 = -619500 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 = -619500 + 624100 Reorder the terms: 624100 + -1580x + x2 = -619500 + 624100 Combine like terms: -619500 + 624100 = 4600 624100 + -1580x + x2 = 4600 Factor a perfect square on the left side: (x + -790)(x + -790) = 4600 Calculate the square root of the right side: 67.823299831 Break this problem into two subproblems by setting (x + -790) equal to 67.823299831 and -67.823299831.Subproblem 1
x + -790 = 67.823299831 Simplifying x + -790 = 67.823299831 Reorder the terms: -790 + x = 67.823299831 Solving -790 + x = 67.823299831 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 = 67.823299831 + 790 Combine like terms: -790 + 790 = 0 0 + x = 67.823299831 + 790 x = 67.823299831 + 790 Combine like terms: 67.823299831 + 790 = 857.823299831 x = 857.823299831 Simplifying x = 857.823299831Subproblem 2
x + -790 = -67.823299831 Simplifying x + -790 = -67.823299831 Reorder the terms: -790 + x = -67.823299831 Solving -790 + x = -67.823299831 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 = -67.823299831 + 790 Combine like terms: -790 + 790 = 0 0 + x = -67.823299831 + 790 x = -67.823299831 + 790 Combine like terms: -67.823299831 + 790 = 722.176700169 x = 722.176700169 Simplifying x = 722.176700169Solution
The solution to the problem is based on the solutions from the subproblems. x = {857.823299831, 722.176700169}
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