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Simplifying 26000 = X2 + -234X + 347 Reorder the terms: 26000 = 347 + -234X + X2 Solving 26000 = 347 + -234X + X2 Solving for variable 'X'. Combine like terms: 26000 + -347 = 25653 25653 + 234X + -1X2 = 347 + -234X + X2 + -347 + 234X + -1X2 Reorder the terms: 25653 + 234X + -1X2 = 347 + -347 + -234X + 234X + X2 + -1X2 Combine like terms: 347 + -347 = 0 25653 + 234X + -1X2 = 0 + -234X + 234X + X2 + -1X2 25653 + 234X + -1X2 = -234X + 234X + X2 + -1X2 Combine like terms: -234X + 234X = 0 25653 + 234X + -1X2 = 0 + X2 + -1X2 25653 + 234X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 25653 + 234X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25653 + -234X + X2 = 0 Move the constant term to the right: Add '25653' to each side of the equation. -25653 + -234X + 25653 + X2 = 0 + 25653 Reorder the terms: -25653 + 25653 + -234X + X2 = 0 + 25653 Combine like terms: -25653 + 25653 = 0 0 + -234X + X2 = 0 + 25653 -234X + X2 = 0 + 25653 Combine like terms: 0 + 25653 = 25653 -234X + X2 = 25653 The X term is -234X. Take half its coefficient (-117). Square it (13689) and add it to both sides. Add '13689' to each side of the equation. -234X + 13689 + X2 = 25653 + 13689 Reorder the terms: 13689 + -234X + X2 = 25653 + 13689 Combine like terms: 25653 + 13689 = 39342 13689 + -234X + X2 = 39342 Factor a perfect square on the left side: (X + -117)(X + -117) = 39342 Calculate the square root of the right side: 198.348178716 Break this problem into two subproblems by setting (X + -117) equal to 198.348178716 and -198.348178716.Subproblem 1
X + -117 = 198.348178716 Simplifying X + -117 = 198.348178716 Reorder the terms: -117 + X = 198.348178716 Solving -117 + X = 198.348178716 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '117' to each side of the equation. -117 + 117 + X = 198.348178716 + 117 Combine like terms: -117 + 117 = 0 0 + X = 198.348178716 + 117 X = 198.348178716 + 117 Combine like terms: 198.348178716 + 117 = 315.348178716 X = 315.348178716 Simplifying X = 315.348178716Subproblem 2
X + -117 = -198.348178716 Simplifying X + -117 = -198.348178716 Reorder the terms: -117 + X = -198.348178716 Solving -117 + X = -198.348178716 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '117' to each side of the equation. -117 + 117 + X = -198.348178716 + 117 Combine like terms: -117 + 117 = 0 0 + X = -198.348178716 + 117 X = -198.348178716 + 117 Combine like terms: -198.348178716 + 117 = -81.348178716 X = -81.348178716 Simplifying X = -81.348178716Solution
The solution to the problem is based on the solutions from the subproblems. X = {315.348178716, -81.348178716}
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