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Simplifying 0.99x2 + 233.6x + -13836 = 0 Reorder the terms: -13836 + 233.6x + 0.99x2 = 0 Solving -13836 + 233.6x + 0.99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.99 the coefficient of the squared term: Divide each side by '0.99'. -13975.75758 + 235.959596x + x2 = 0 Move the constant term to the right: Add '13975.75758' to each side of the equation. -13975.75758 + 235.959596x + 13975.75758 + x2 = 0 + 13975.75758 Reorder the terms: -13975.75758 + 13975.75758 + 235.959596x + x2 = 0 + 13975.75758 Combine like terms: -13975.75758 + 13975.75758 = 0.00000 0.00000 + 235.959596x + x2 = 0 + 13975.75758 235.959596x + x2 = 0 + 13975.75758 Combine like terms: 0 + 13975.75758 = 13975.75758 235.959596x + x2 = 13975.75758 The x term is 235.959596x. Take half its coefficient (117.979798). Square it (13919.23274) and add it to both sides. Add '13919.23274' to each side of the equation. 235.959596x + 13919.23274 + x2 = 13975.75758 + 13919.23274 Reorder the terms: 13919.23274 + 235.959596x + x2 = 13975.75758 + 13919.23274 Combine like terms: 13975.75758 + 13919.23274 = 27894.99032 13919.23274 + 235.959596x + x2 = 27894.99032 Factor a perfect square on the left side: (x + 117.979798)(x + 117.979798) = 27894.99032 Calculate the square root of the right side: 167.017934127 Break this problem into two subproblems by setting (x + 117.979798) equal to 167.017934127 and -167.017934127.Subproblem 1
x + 117.979798 = 167.017934127 Simplifying x + 117.979798 = 167.017934127 Reorder the terms: 117.979798 + x = 167.017934127 Solving 117.979798 + x = 167.017934127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-117.979798' to each side of the equation. 117.979798 + -117.979798 + x = 167.017934127 + -117.979798 Combine like terms: 117.979798 + -117.979798 = 0.000000 0.000000 + x = 167.017934127 + -117.979798 x = 167.017934127 + -117.979798 Combine like terms: 167.017934127 + -117.979798 = 49.038136127 x = 49.038136127 Simplifying x = 49.038136127Subproblem 2
x + 117.979798 = -167.017934127 Simplifying x + 117.979798 = -167.017934127 Reorder the terms: 117.979798 + x = -167.017934127 Solving 117.979798 + x = -167.017934127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-117.979798' to each side of the equation. 117.979798 + -117.979798 + x = -167.017934127 + -117.979798 Combine like terms: 117.979798 + -117.979798 = 0.000000 0.000000 + x = -167.017934127 + -117.979798 x = -167.017934127 + -117.979798 Combine like terms: -167.017934127 + -117.979798 = -284.997732127 x = -284.997732127 Simplifying x = -284.997732127Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.038136127, -284.997732127}
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