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Simplifying 100 + 29X + -1X2 = 0 Solving 100 + 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'. -100 + -29X + X2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -29X + 100 + X2 = 0 + 100 Reorder the terms: -100 + 100 + -29X + X2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -29X + X2 = 0 + 100 -29X + X2 = 0 + 100 Combine like terms: 0 + 100 = 100 -29X + X2 = 100 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 = 100 + 210.25 Reorder the terms: 210.25 + -29X + X2 = 100 + 210.25 Combine like terms: 100 + 210.25 = 310.25 210.25 + -29X + X2 = 310.25 Factor a perfect square on the left side: (X + -14.5)(X + -14.5) = 310.25 Calculate the square root of the right side: 17.613914954 Break this problem into two subproblems by setting (X + -14.5) equal to 17.613914954 and -17.613914954.Subproblem 1
X + -14.5 = 17.613914954 Simplifying X + -14.5 = 17.613914954 Reorder the terms: -14.5 + X = 17.613914954 Solving -14.5 + X = 17.613914954 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 = 17.613914954 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + X = 17.613914954 + 14.5 X = 17.613914954 + 14.5 Combine like terms: 17.613914954 + 14.5 = 32.113914954 X = 32.113914954 Simplifying X = 32.113914954Subproblem 2
X + -14.5 = -17.613914954 Simplifying X + -14.5 = -17.613914954 Reorder the terms: -14.5 + X = -17.613914954 Solving -14.5 + X = -17.613914954 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 = -17.613914954 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + X = -17.613914954 + 14.5 X = -17.613914954 + 14.5 Combine like terms: -17.613914954 + 14.5 = -3.113914954 X = -3.113914954 Simplifying X = -3.113914954Solution
The solution to the problem is based on the solutions from the subproblems. X = {32.113914954, -3.113914954}
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