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Simplifying x2 + -126x + 1296 = 0 Reorder the terms: 1296 + -126x + x2 = 0 Solving 1296 + -126x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1296' to each side of the equation. 1296 + -126x + -1296 + x2 = 0 + -1296 Reorder the terms: 1296 + -1296 + -126x + x2 = 0 + -1296 Combine like terms: 1296 + -1296 = 0 0 + -126x + x2 = 0 + -1296 -126x + x2 = 0 + -1296 Combine like terms: 0 + -1296 = -1296 -126x + x2 = -1296 The x term is -126x. Take half its coefficient (-63). Square it (3969) and add it to both sides. Add '3969' to each side of the equation. -126x + 3969 + x2 = -1296 + 3969 Reorder the terms: 3969 + -126x + x2 = -1296 + 3969 Combine like terms: -1296 + 3969 = 2673 3969 + -126x + x2 = 2673 Factor a perfect square on the left side: (x + -63)(x + -63) = 2673 Calculate the square root of the right side: 51.701063819 Break this problem into two subproblems by setting (x + -63) equal to 51.701063819 and -51.701063819.Subproblem 1
x + -63 = 51.701063819 Simplifying x + -63 = 51.701063819 Reorder the terms: -63 + x = 51.701063819 Solving -63 + x = 51.701063819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '63' to each side of the equation. -63 + 63 + x = 51.701063819 + 63 Combine like terms: -63 + 63 = 0 0 + x = 51.701063819 + 63 x = 51.701063819 + 63 Combine like terms: 51.701063819 + 63 = 114.701063819 x = 114.701063819 Simplifying x = 114.701063819Subproblem 2
x + -63 = -51.701063819 Simplifying x + -63 = -51.701063819 Reorder the terms: -63 + x = -51.701063819 Solving -63 + x = -51.701063819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '63' to each side of the equation. -63 + 63 + x = -51.701063819 + 63 Combine like terms: -63 + 63 = 0 0 + x = -51.701063819 + 63 x = -51.701063819 + 63 Combine like terms: -51.701063819 + 63 = 11.298936181 x = 11.298936181 Simplifying x = 11.298936181Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.701063819, 11.298936181}
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