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Simplifying x2 + 16x + 17 = 0 Reorder the terms: 17 + 16x + x2 = 0 Solving 17 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 16x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 16x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 16x + x2 = 0 + -17 16x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 16x + x2 = -17 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 = -17 + 64 Reorder the terms: 64 + 16x + x2 = -17 + 64 Combine like terms: -17 + 64 = 47 64 + 16x + x2 = 47 Factor a perfect square on the left side: (x + 8)(x + 8) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + 8) equal to 6.8556546 and -6.8556546.Subproblem 1
x + 8 = 6.8556546 Simplifying x + 8 = 6.8556546 Reorder the terms: 8 + x = 6.8556546 Solving 8 + x = 6.8556546 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 = 6.8556546 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.8556546 + -8 x = 6.8556546 + -8 Combine like terms: 6.8556546 + -8 = -1.1443454 x = -1.1443454 Simplifying x = -1.1443454Subproblem 2
x + 8 = -6.8556546 Simplifying x + 8 = -6.8556546 Reorder the terms: 8 + x = -6.8556546 Solving 8 + x = -6.8556546 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 = -6.8556546 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.8556546 + -8 x = -6.8556546 + -8 Combine like terms: -6.8556546 + -8 = -14.8556546 x = -14.8556546 Simplifying x = -14.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.1443454, -14.8556546}
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