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Simplifying 100x2 + 11258x + -5066104.5 = 0 Reorder the terms: -5066104.5 + 11258x + 100x2 = 0 Solving -5066104.5 + 11258x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -50661.045 + 112.58x + x2 = 0 Move the constant term to the right: Add '50661.045' to each side of the equation. -50661.045 + 112.58x + 50661.045 + x2 = 0 + 50661.045 Reorder the terms: -50661.045 + 50661.045 + 112.58x + x2 = 0 + 50661.045 Combine like terms: -50661.045 + 50661.045 = 0.000 0.000 + 112.58x + x2 = 0 + 50661.045 112.58x + x2 = 0 + 50661.045 Combine like terms: 0 + 50661.045 = 50661.045 112.58x + x2 = 50661.045 The x term is 112.58x. Take half its coefficient (56.29). Square it (3168.5641) and add it to both sides. Add '3168.5641' to each side of the equation. 112.58x + 3168.5641 + x2 = 50661.045 + 3168.5641 Reorder the terms: 3168.5641 + 112.58x + x2 = 50661.045 + 3168.5641 Combine like terms: 50661.045 + 3168.5641 = 53829.6091 3168.5641 + 112.58x + x2 = 53829.6091 Factor a perfect square on the left side: (x + 56.29)(x + 56.29) = 53829.6091 Calculate the square root of the right side: 232.012088263 Break this problem into two subproblems by setting (x + 56.29) equal to 232.012088263 and -232.012088263.Subproblem 1
x + 56.29 = 232.012088263 Simplifying x + 56.29 = 232.012088263 Reorder the terms: 56.29 + x = 232.012088263 Solving 56.29 + x = 232.012088263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56.29' to each side of the equation. 56.29 + -56.29 + x = 232.012088263 + -56.29 Combine like terms: 56.29 + -56.29 = 0.00 0.00 + x = 232.012088263 + -56.29 x = 232.012088263 + -56.29 Combine like terms: 232.012088263 + -56.29 = 175.722088263 x = 175.722088263 Simplifying x = 175.722088263Subproblem 2
x + 56.29 = -232.012088263 Simplifying x + 56.29 = -232.012088263 Reorder the terms: 56.29 + x = -232.012088263 Solving 56.29 + x = -232.012088263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-56.29' to each side of the equation. 56.29 + -56.29 + x = -232.012088263 + -56.29 Combine like terms: 56.29 + -56.29 = 0.00 0.00 + x = -232.012088263 + -56.29 x = -232.012088263 + -56.29 Combine like terms: -232.012088263 + -56.29 = -288.302088263 x = -288.302088263 Simplifying x = -288.302088263Solution
The solution to the problem is based on the solutions from the subproblems. x = {175.722088263, -288.302088263}
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