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Simplifying x2 + 16x + -50 = 0 Reorder the terms: -50 + 16x + x2 = 0 Solving -50 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 16x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 16x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 16x + x2 = 0 + 50 16x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 16x + x2 = 50 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 = 50 + 64 Reorder the terms: 64 + 16x + x2 = 50 + 64 Combine like terms: 50 + 64 = 114 64 + 16x + x2 = 114 Factor a perfect square on the left side: (x + 8)(x + 8) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + 8) equal to 10.677078252 and -10.677078252.Subproblem 1
x + 8 = 10.677078252 Simplifying x + 8 = 10.677078252 Reorder the terms: 8 + x = 10.677078252 Solving 8 + x = 10.677078252 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 = 10.677078252 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.677078252 + -8 x = 10.677078252 + -8 Combine like terms: 10.677078252 + -8 = 2.677078252 x = 2.677078252 Simplifying x = 2.677078252Subproblem 2
x + 8 = -10.677078252 Simplifying x + 8 = -10.677078252 Reorder the terms: 8 + x = -10.677078252 Solving 8 + x = -10.677078252 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 = -10.677078252 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.677078252 + -8 x = -10.677078252 + -8 Combine like terms: -10.677078252 + -8 = -18.677078252 x = -18.677078252 Simplifying x = -18.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.677078252, -18.677078252}
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