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Simplifying x2 + 10x + -1100 = 0 Reorder the terms: -1100 + 10x + x2 = 0 Solving -1100 + 10x + 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 + 10x + 1100 + x2 = 0 + 1100 Reorder the terms: -1100 + 1100 + 10x + x2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + 10x + x2 = 0 + 1100 10x + x2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 10x + x2 = 1100 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 1100 + 25 Reorder the terms: 25 + 10x + x2 = 1100 + 25 Combine like terms: 1100 + 25 = 1125 25 + 10x + x2 = 1125 Factor a perfect square on the left side: (x + 5)(x + 5) = 1125 Calculate the square root of the right side: 33.541019662 Break this problem into two subproblems by setting (x + 5) equal to 33.541019662 and -33.541019662.Subproblem 1
x + 5 = 33.541019662 Simplifying x + 5 = 33.541019662 Reorder the terms: 5 + x = 33.541019662 Solving 5 + x = 33.541019662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 33.541019662 + -5 Combine like terms: 5 + -5 = 0 0 + x = 33.541019662 + -5 x = 33.541019662 + -5 Combine like terms: 33.541019662 + -5 = 28.541019662 x = 28.541019662 Simplifying x = 28.541019662Subproblem 2
x + 5 = -33.541019662 Simplifying x + 5 = -33.541019662 Reorder the terms: 5 + x = -33.541019662 Solving 5 + x = -33.541019662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -33.541019662 + -5 Combine like terms: 5 + -5 = 0 0 + x = -33.541019662 + -5 x = -33.541019662 + -5 Combine like terms: -33.541019662 + -5 = -38.541019662 x = -38.541019662 Simplifying x = -38.541019662Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.541019662, -38.541019662}
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