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Simplifying 2x10 + 275x5 + 243 = 0 Reorder the terms: 243 + 275x5 + 2x10 = 0 Solving 243 + 275x5 + 2x10 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 121.5 + 137.5x5 + x10 = 0 Move the constant term to the right: Add '-121.5' to each side of the equation. 121.5 + 137.5x5 + -121.5 + x10 = 0 + -121.5 Reorder the terms: 121.5 + -121.5 + 137.5x5 + x10 = 0 + -121.5 Combine like terms: 121.5 + -121.5 = 0.0 0.0 + 137.5x5 + x10 = 0 + -121.5 137.5x5 + x10 = 0 + -121.5 Combine like terms: 0 + -121.5 = -121.5 137.5x5 + x10 = -121.5 The x term is 137.5x5. Take half its coefficient (68.75). Square it (4726.5625) and add it to both sides. Add '4726.5625' to each side of the equation. 137.5x5 + 4726.5625 + x10 = -121.5 + 4726.5625 Reorder the terms: 4726.5625 + 137.5x5 + x10 = -121.5 + 4726.5625 Combine like terms: -121.5 + 4726.5625 = 4605.0625 4726.5625 + 137.5x5 + x10 = 4605.0625 Factor a perfect square on the left side: (x5 + 68.75)(x5 + 68.75) = 4605.0625 Calculate the square root of the right side: 67.860610814 Break this problem into two subproblems by setting (x5 + 68.75) equal to 67.860610814 and -67.860610814.Subproblem 1
x5 + 68.75 = 67.860610814 Simplifying x5 + 68.75 = 67.860610814 Reorder the terms: 68.75 + x5 = 67.860610814 Solving 68.75 + x5 = 67.860610814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-68.75' to each side of the equation. 68.75 + -68.75 + x5 = 67.860610814 + -68.75 Combine like terms: 68.75 + -68.75 = 0.00 0.00 + x5 = 67.860610814 + -68.75 x5 = 67.860610814 + -68.75 Combine like terms: 67.860610814 + -68.75 = -0.889389186 x5 = -0.889389186 Simplifying x5 = -0.889389186 Reorder the terms: 0.889389186 + x5 = -0.889389186 + 0.889389186 Combine like terms: -0.889389186 + 0.889389186 = 0.000000000 0.889389186 + x5 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x5 + 68.75 = -67.860610814 Simplifying x5 + 68.75 = -67.860610814 Reorder the terms: 68.75 + x5 = -67.860610814 Solving 68.75 + x5 = -67.860610814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-68.75' to each side of the equation. 68.75 + -68.75 + x5 = -67.860610814 + -68.75 Combine like terms: 68.75 + -68.75 = 0.00 0.00 + x5 = -67.860610814 + -68.75 x5 = -67.860610814 + -68.75 Combine like terms: -67.860610814 + -68.75 = -136.610610814 x5 = -136.610610814 Simplifying x5 = -136.610610814 Reorder the terms: 136.610610814 + x5 = -136.610610814 + 136.610610814 Combine like terms: -136.610610814 + 136.610610814 = 0.000000000 136.610610814 + x5 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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