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Simplifying x2 + 16x + -1100 = 0 Reorder the terms: -1100 + 16x + x2 = 0 Solving -1100 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1100' to each side of the equation. -1100 + 16x + 1100 + x2 = 0 + 1100 Reorder the terms: -1100 + 1100 + 16x + x2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + 16x + x2 = 0 + 1100 16x + x2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 16x + x2 = 1100 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 = 1100 + 64 Reorder the terms: 64 + 16x + x2 = 1100 + 64 Combine like terms: 1100 + 64 = 1164 64 + 16x + x2 = 1164 Factor a perfect square on the left side: (x + 8)(x + 8) = 1164 Calculate the square root of the right side: 34.117444218 Break this problem into two subproblems by setting (x + 8) equal to 34.117444218 and -34.117444218.Subproblem 1
x + 8 = 34.117444218 Simplifying x + 8 = 34.117444218 Reorder the terms: 8 + x = 34.117444218 Solving 8 + x = 34.117444218 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 = 34.117444218 + -8 Combine like terms: 8 + -8 = 0 0 + x = 34.117444218 + -8 x = 34.117444218 + -8 Combine like terms: 34.117444218 + -8 = 26.117444218 x = 26.117444218 Simplifying x = 26.117444218Subproblem 2
x + 8 = -34.117444218 Simplifying x + 8 = -34.117444218 Reorder the terms: 8 + x = -34.117444218 Solving 8 + x = -34.117444218 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 = -34.117444218 + -8 Combine like terms: 8 + -8 = 0 0 + x = -34.117444218 + -8 x = -34.117444218 + -8 Combine like terms: -34.117444218 + -8 = -42.117444218 x = -42.117444218 Simplifying x = -42.117444218Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.117444218, -42.117444218}
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