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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 = 7.747340124 x = 7.747340124 Simplifying x = 7.747340124Subproblem 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 = -15.747340124 x = -15.747340124 Simplifying x = -15.747340124Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.747340124, -15.747340124}
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