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Simplifying -1x2 + 29x + 222 = 0 Reorder the terms: 222 + 29x + -1x2 = 0 Solving 222 + 29x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -222 + -29x + x2 = 0 Move the constant term to the right: Add '222' to each side of the equation. -222 + -29x + 222 + x2 = 0 + 222 Reorder the terms: -222 + 222 + -29x + x2 = 0 + 222 Combine like terms: -222 + 222 = 0 0 + -29x + x2 = 0 + 222 -29x + x2 = 0 + 222 Combine like terms: 0 + 222 = 222 -29x + x2 = 222 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = 222 + 210.25 Reorder the terms: 210.25 + -29x + x2 = 222 + 210.25 Combine like terms: 222 + 210.25 = 432.25 210.25 + -29x + x2 = 432.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 432.25 Calculate the square root of the right side: 20.790622886 Break this problem into two subproblems by setting (x + -14.5) equal to 20.790622886 and -20.790622886.Subproblem 1
x + -14.5 = 20.790622886 Simplifying x + -14.5 = 20.790622886 Reorder the terms: -14.5 + x = 20.790622886 Solving -14.5 + x = 20.790622886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 20.790622886 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 20.790622886 + 14.5 x = 20.790622886 + 14.5 Combine like terms: 20.790622886 + 14.5 = 35.290622886 x = 35.290622886 Simplifying x = 35.290622886Subproblem 2
x + -14.5 = -20.790622886 Simplifying x + -14.5 = -20.790622886 Reorder the terms: -14.5 + x = -20.790622886 Solving -14.5 + x = -20.790622886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -20.790622886 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -20.790622886 + 14.5 x = -20.790622886 + 14.5 Combine like terms: -20.790622886 + 14.5 = -6.290622886 x = -6.290622886 Simplifying x = -6.290622886Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.290622886, -6.290622886}
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