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Simplifying 0.00027232x2 + -0.0013793x + -0.028893 = 0 Reorder the terms: -0.028893 + -0.0013793x + 0.00027232x2 = 0 Solving -0.028893 + -0.0013793x + 0.00027232x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.00027232 the coefficient of the squared term: Divide each side by '0.00027232'. -106.0994418 + -5.064997062x + x2 = 0 Move the constant term to the right: Add '106.0994418' to each side of the equation. -106.0994418 + -5.064997062x + 106.0994418 + x2 = 0 + 106.0994418 Reorder the terms: -106.0994418 + 106.0994418 + -5.064997062x + x2 = 0 + 106.0994418 Combine like terms: -106.0994418 + 106.0994418 = 0.0000000 0.0000000 + -5.064997062x + x2 = 0 + 106.0994418 -5.064997062x + x2 = 0 + 106.0994418 Combine like terms: 0 + 106.0994418 = 106.0994418 -5.064997062x + x2 = 106.0994418 The x term is -5.064997062x. Take half its coefficient (-2.532498531). Square it (6.413548810) and add it to both sides. Add '6.413548810' to each side of the equation. -5.064997062x + 6.413548810 + x2 = 106.0994418 + 6.413548810 Reorder the terms: 6.413548810 + -5.064997062x + x2 = 106.0994418 + 6.413548810 Combine like terms: 106.0994418 + 6.413548810 = 112.51299061 6.413548810 + -5.064997062x + x2 = 112.51299061 Factor a perfect square on the left side: (x + -2.532498531)(x + -2.532498531) = 112.51299061 Calculate the square root of the right side: 10.607214083 Break this problem into two subproblems by setting (x + -2.532498531) equal to 10.607214083 and -10.607214083.Subproblem 1
x + -2.532498531 = 10.607214083 Simplifying x + -2.532498531 = 10.607214083 Reorder the terms: -2.532498531 + x = 10.607214083 Solving -2.532498531 + x = 10.607214083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.532498531' to each side of the equation. -2.532498531 + 2.532498531 + x = 10.607214083 + 2.532498531 Combine like terms: -2.532498531 + 2.532498531 = 0.000000000 0.000000000 + x = 10.607214083 + 2.532498531 x = 10.607214083 + 2.532498531 Combine like terms: 10.607214083 + 2.532498531 = 13.139712614 x = 13.139712614 Simplifying x = 13.139712614Subproblem 2
x + -2.532498531 = -10.607214083 Simplifying x + -2.532498531 = -10.607214083 Reorder the terms: -2.532498531 + x = -10.607214083 Solving -2.532498531 + x = -10.607214083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.532498531' to each side of the equation. -2.532498531 + 2.532498531 + x = -10.607214083 + 2.532498531 Combine like terms: -2.532498531 + 2.532498531 = 0.000000000 0.000000000 + x = -10.607214083 + 2.532498531 x = -10.607214083 + 2.532498531 Combine like terms: -10.607214083 + 2.532498531 = -8.074715552 x = -8.074715552 Simplifying x = -8.074715552Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.139712614, -8.074715552}
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