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Simplifying x2 + -8x + -122 = 0 Reorder the terms: -122 + -8x + x2 = 0 Solving -122 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + -8x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + -8x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + -8x + x2 = 0 + 122 -8x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 -8x + x2 = 122 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 122 + 16 Reorder the terms: 16 + -8x + x2 = 122 + 16 Combine like terms: 122 + 16 = 138 16 + -8x + x2 = 138 Factor a perfect square on the left side: (x + -4)(x + -4) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (x + -4) equal to 11.747340124 and -11.747340124.Subproblem 1
x + -4 = 11.747340124 Simplifying x + -4 = 11.747340124 Reorder the terms: -4 + x = 11.747340124 Solving -4 + x = 11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 11.747340124 + 4 Combine like terms: -4 + 4 = 0 0 + x = 11.747340124 + 4 x = 11.747340124 + 4 Combine like terms: 11.747340124 + 4 = 15.747340124 x = 15.747340124 Simplifying x = 15.747340124Subproblem 2
x + -4 = -11.747340124 Simplifying x + -4 = -11.747340124 Reorder the terms: -4 + x = -11.747340124 Solving -4 + x = -11.747340124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -11.747340124 + 4 Combine like terms: -4 + 4 = 0 0 + x = -11.747340124 + 4 x = -11.747340124 + 4 Combine like terms: -11.747340124 + 4 = -7.747340124 x = -7.747340124 Simplifying x = -7.747340124Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.747340124, -7.747340124}
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