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Simplifying x2 + 16x + -140 = 0 Reorder the terms: -140 + 16x + x2 = 0 Solving -140 + 16x + 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 + 16x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 16x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 16x + x2 = 0 + 140 16x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 16x + x2 = 140 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 140 + 64 Reorder the terms: 64 + 16x + x2 = 140 + 64 Combine like terms: 140 + 64 = 204 64 + 16x + x2 = 204 Factor a perfect square on the left side: (x + 8)(x + 8) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + 8) equal to 14.282856857 and -14.282856857.Subproblem 1
x + 8 = 14.282856857 Simplifying x + 8 = 14.282856857 Reorder the terms: 8 + x = 14.282856857 Solving 8 + x = 14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 14.282856857 + -8 Combine like terms: 8 + -8 = 0 0 + x = 14.282856857 + -8 x = 14.282856857 + -8 Combine like terms: 14.282856857 + -8 = 6.282856857 x = 6.282856857 Simplifying x = 6.282856857Subproblem 2
x + 8 = -14.282856857 Simplifying x + 8 = -14.282856857 Reorder the terms: 8 + x = -14.282856857 Solving 8 + x = -14.282856857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -14.282856857 + -8 Combine like terms: 8 + -8 = 0 0 + x = -14.282856857 + -8 x = -14.282856857 + -8 Combine like terms: -14.282856857 + -8 = -22.282856857 x = -22.282856857 Simplifying x = -22.282856857Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.282856857, -22.282856857}
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