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Simplifying x2 + 16x + -14 = 0 Reorder the terms: -14 + 16x + x2 = 0 Solving -14 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 16x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 16x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 16x + x2 = 0 + 14 16x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 16x + x2 = 14 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 = 14 + 64 Reorder the terms: 64 + 16x + x2 = 14 + 64 Combine like terms: 14 + 64 = 78 64 + 16x + x2 = 78 Factor a perfect square on the left side: (x + 8)(x + 8) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + 8) equal to 8.831760866 and -8.831760866.Subproblem 1
x + 8 = 8.831760866 Simplifying x + 8 = 8.831760866 Reorder the terms: 8 + x = 8.831760866 Solving 8 + x = 8.831760866 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 = 8.831760866 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.831760866 + -8 x = 8.831760866 + -8 Combine like terms: 8.831760866 + -8 = 0.831760866 x = 0.831760866 Simplifying x = 0.831760866Subproblem 2
x + 8 = -8.831760866 Simplifying x + 8 = -8.831760866 Reorder the terms: 8 + x = -8.831760866 Solving 8 + x = -8.831760866 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 = -8.831760866 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.831760866 + -8 x = -8.831760866 + -8 Combine like terms: -8.831760866 + -8 = -16.831760866 x = -16.831760866 Simplifying x = -16.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.831760866, -16.831760866}
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