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Simplifying x2 + -52x + 140 = 0 Reorder the terms: 140 + -52x + x2 = 0 Solving 140 + -52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-140' to each side of the equation. 140 + -52x + -140 + x2 = 0 + -140 Reorder the terms: 140 + -140 + -52x + x2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + -52x + x2 = 0 + -140 -52x + x2 = 0 + -140 Combine like terms: 0 + -140 = -140 -52x + x2 = -140 The x term is -52x. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52x + 676 + x2 = -140 + 676 Reorder the terms: 676 + -52x + x2 = -140 + 676 Combine like terms: -140 + 676 = 536 676 + -52x + x2 = 536 Factor a perfect square on the left side: (x + -26)(x + -26) = 536 Calculate the square root of the right side: 23.151673806 Break this problem into two subproblems by setting (x + -26) equal to 23.151673806 and -23.151673806.Subproblem 1
x + -26 = 23.151673806 Simplifying x + -26 = 23.151673806 Reorder the terms: -26 + x = 23.151673806 Solving -26 + x = 23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 23.151673806 + 26 Combine like terms: -26 + 26 = 0 0 + x = 23.151673806 + 26 x = 23.151673806 + 26 Combine like terms: 23.151673806 + 26 = 49.151673806 x = 49.151673806 Simplifying x = 49.151673806Subproblem 2
x + -26 = -23.151673806 Simplifying x + -26 = -23.151673806 Reorder the terms: -26 + x = -23.151673806 Solving -26 + x = -23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -23.151673806 + 26 Combine like terms: -26 + 26 = 0 0 + x = -23.151673806 + 26 x = -23.151673806 + 26 Combine like terms: -23.151673806 + 26 = 2.848326194 x = 2.848326194 Simplifying x = 2.848326194Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.151673806, 2.848326194}
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