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Simplifying x2 + 52x + -1020 = 0 Reorder the terms: -1020 + 52x + x2 = 0 Solving -1020 + 52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1020' to each side of the equation. -1020 + 52x + 1020 + x2 = 0 + 1020 Reorder the terms: -1020 + 1020 + 52x + x2 = 0 + 1020 Combine like terms: -1020 + 1020 = 0 0 + 52x + x2 = 0 + 1020 52x + x2 = 0 + 1020 Combine like terms: 0 + 1020 = 1020 52x + x2 = 1020 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 = 1020 + 676 Reorder the terms: 676 + 52x + x2 = 1020 + 676 Combine like terms: 1020 + 676 = 1696 676 + 52x + x2 = 1696 Factor a perfect square on the left side: (x + 26)(x + 26) = 1696 Calculate the square root of the right side: 41.182520564 Break this problem into two subproblems by setting (x + 26) equal to 41.182520564 and -41.182520564.Subproblem 1
x + 26 = 41.182520564 Simplifying x + 26 = 41.182520564 Reorder the terms: 26 + x = 41.182520564 Solving 26 + x = 41.182520564 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 = 41.182520564 + -26 Combine like terms: 26 + -26 = 0 0 + x = 41.182520564 + -26 x = 41.182520564 + -26 Combine like terms: 41.182520564 + -26 = 15.182520564 x = 15.182520564 Simplifying x = 15.182520564Subproblem 2
x + 26 = -41.182520564 Simplifying x + 26 = -41.182520564 Reorder the terms: 26 + x = -41.182520564 Solving 26 + x = -41.182520564 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 = -41.182520564 + -26 Combine like terms: 26 + -26 = 0 0 + x = -41.182520564 + -26 x = -41.182520564 + -26 Combine like terms: -41.182520564 + -26 = -67.182520564 x = -67.182520564 Simplifying x = -67.182520564Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.182520564, -67.182520564}
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