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Simplifying 100X + 1000 = 1035.67X2 Reorder the terms: 1000 + 100X = 1035.67X2 Solving 1000 + 100X = 1035.67X2 Solving for variable 'X'. Combine like terms: 1035.67X2 + -1035.67X2 = 0.00 1000 + 100X + -1035.67X2 = 0.00 Begin completing the square. Divide all terms by -1035.67 the coefficient of the squared term: Divide each side by '-1035.67'. -0.9655585273 + -0.09655585273X + X2 = 0 Move the constant term to the right: Add '0.9655585273' to each side of the equation. -0.9655585273 + -0.09655585273X + 0.9655585273 + X2 = 0 + 0.9655585273 Reorder the terms: -0.9655585273 + 0.9655585273 + -0.09655585273X + X2 = 0 + 0.9655585273 Combine like terms: -0.9655585273 + 0.9655585273 = 0.0000000000 0.0000000000 + -0.09655585273X + X2 = 0 + 0.9655585273 -0.09655585273X + X2 = 0 + 0.9655585273 Combine like terms: 0 + 0.9655585273 = 0.9655585273 -0.09655585273X + X2 = 0.9655585273 The X term is -0.09655585273X. Take half its coefficient (-0.04827792637). Square it (0.002330758175) and add it to both sides. Add '0.002330758175' to each side of the equation. -0.09655585273X + 0.002330758175 + X2 = 0.9655585273 + 0.002330758175 Reorder the terms: 0.002330758175 + -0.09655585273X + X2 = 0.9655585273 + 0.002330758175 Combine like terms: 0.9655585273 + 0.002330758175 = 0.967889285475 0.002330758175 + -0.09655585273X + X2 = 0.967889285475 Factor a perfect square on the left side: (X + -0.04827792637)(X + -0.04827792637) = 0.967889285475 Calculate the square root of the right side: 0.983813644 Break this problem into two subproblems by setting (X + -0.04827792637) equal to 0.983813644 and -0.983813644.Subproblem 1
X + -0.04827792637 = 0.983813644 Simplifying X + -0.04827792637 = 0.983813644 Reorder the terms: -0.04827792637 + X = 0.983813644 Solving -0.04827792637 + X = 0.983813644 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.04827792637' to each side of the equation. -0.04827792637 + 0.04827792637 + X = 0.983813644 + 0.04827792637 Combine like terms: -0.04827792637 + 0.04827792637 = 0.00000000000 0.00000000000 + X = 0.983813644 + 0.04827792637 X = 0.983813644 + 0.04827792637 Combine like terms: 0.983813644 + 0.04827792637 = 1.03209157037 X = 1.03209157037 Simplifying X = 1.03209157037Subproblem 2
X + -0.04827792637 = -0.983813644 Simplifying X + -0.04827792637 = -0.983813644 Reorder the terms: -0.04827792637 + X = -0.983813644 Solving -0.04827792637 + X = -0.983813644 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.04827792637' to each side of the equation. -0.04827792637 + 0.04827792637 + X = -0.983813644 + 0.04827792637 Combine like terms: -0.04827792637 + 0.04827792637 = 0.00000000000 0.00000000000 + X = -0.983813644 + 0.04827792637 X = -0.983813644 + 0.04827792637 Combine like terms: -0.983813644 + 0.04827792637 = -0.93553571763 X = -0.93553571763 Simplifying X = -0.93553571763Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.03209157037, -0.93553571763}
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