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Simplifying x2 + 16x + -27 = 0 Reorder the terms: -27 + 16x + x2 = 0 Solving -27 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 16x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 16x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 16x + x2 = 0 + 27 16x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 16x + x2 = 27 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 = 27 + 64 Reorder the terms: 64 + 16x + x2 = 27 + 64 Combine like terms: 27 + 64 = 91 64 + 16x + x2 = 91 Factor a perfect square on the left side: (x + 8)(x + 8) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + 8) equal to 9.539392014 and -9.539392014.Subproblem 1
x + 8 = 9.539392014 Simplifying x + 8 = 9.539392014 Reorder the terms: 8 + x = 9.539392014 Solving 8 + x = 9.539392014 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 = 9.539392014 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.539392014 + -8 x = 9.539392014 + -8 Combine like terms: 9.539392014 + -8 = 1.539392014 x = 1.539392014 Simplifying x = 1.539392014Subproblem 2
x + 8 = -9.539392014 Simplifying x + 8 = -9.539392014 Reorder the terms: 8 + x = -9.539392014 Solving 8 + x = -9.539392014 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 = -9.539392014 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.539392014 + -8 x = -9.539392014 + -8 Combine like terms: -9.539392014 + -8 = -17.539392014 x = -17.539392014 Simplifying x = -17.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.539392014, -17.539392014}
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