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Simplifying 26x2 + 808x + -10637 = 0 Reorder the terms: -10637 + 808x + 26x2 = 0 Solving -10637 + 808x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -409.1153846 + 31.07692308x + x2 = 0 Move the constant term to the right: Add '409.1153846' to each side of the equation. -409.1153846 + 31.07692308x + 409.1153846 + x2 = 0 + 409.1153846 Reorder the terms: -409.1153846 + 409.1153846 + 31.07692308x + x2 = 0 + 409.1153846 Combine like terms: -409.1153846 + 409.1153846 = 0.0000000 0.0000000 + 31.07692308x + x2 = 0 + 409.1153846 31.07692308x + x2 = 0 + 409.1153846 Combine like terms: 0 + 409.1153846 = 409.1153846 31.07692308x + x2 = 409.1153846 The x term is 31.07692308x. Take half its coefficient (15.53846154). Square it (241.4437870) and add it to both sides. Add '241.4437870' to each side of the equation. 31.07692308x + 241.4437870 + x2 = 409.1153846 + 241.4437870 Reorder the terms: 241.4437870 + 31.07692308x + x2 = 409.1153846 + 241.4437870 Combine like terms: 409.1153846 + 241.4437870 = 650.5591716 241.4437870 + 31.07692308x + x2 = 650.5591716 Factor a perfect square on the left side: (x + 15.53846154)(x + 15.53846154) = 650.5591716 Calculate the square root of the right side: 25.506061468 Break this problem into two subproblems by setting (x + 15.53846154) equal to 25.506061468 and -25.506061468.Subproblem 1
x + 15.53846154 = 25.506061468 Simplifying x + 15.53846154 = 25.506061468 Reorder the terms: 15.53846154 + x = 25.506061468 Solving 15.53846154 + x = 25.506061468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.53846154' to each side of the equation. 15.53846154 + -15.53846154 + x = 25.506061468 + -15.53846154 Combine like terms: 15.53846154 + -15.53846154 = 0.00000000 0.00000000 + x = 25.506061468 + -15.53846154 x = 25.506061468 + -15.53846154 Combine like terms: 25.506061468 + -15.53846154 = 9.967599928 x = 9.967599928 Simplifying x = 9.967599928Subproblem 2
x + 15.53846154 = -25.506061468 Simplifying x + 15.53846154 = -25.506061468 Reorder the terms: 15.53846154 + x = -25.506061468 Solving 15.53846154 + x = -25.506061468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.53846154' to each side of the equation. 15.53846154 + -15.53846154 + x = -25.506061468 + -15.53846154 Combine like terms: 15.53846154 + -15.53846154 = 0.00000000 0.00000000 + x = -25.506061468 + -15.53846154 x = -25.506061468 + -15.53846154 Combine like terms: -25.506061468 + -15.53846154 = -41.044523008 x = -41.044523008 Simplifying x = -41.044523008Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.967599928, -41.044523008}
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