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Simplifying x + 5 = -1x2 + 14x + 49 Reorder the terms: 5 + x = -1x2 + 14x + 49 Reorder the terms: 5 + x = 49 + 14x + -1x2 Solving 5 + x = 49 + 14x + -1x2 Solving for variable 'x'. Reorder the terms: 5 + -49 + x + -14x + x2 = 49 + 14x + -1x2 + -49 + -14x + x2 Combine like terms: 5 + -49 = -44 -44 + x + -14x + x2 = 49 + 14x + -1x2 + -49 + -14x + x2 Combine like terms: x + -14x = -13x -44 + -13x + x2 = 49 + 14x + -1x2 + -49 + -14x + x2 Reorder the terms: -44 + -13x + x2 = 49 + -49 + 14x + -14x + -1x2 + x2 Combine like terms: 49 + -49 = 0 -44 + -13x + x2 = 0 + 14x + -14x + -1x2 + x2 -44 + -13x + x2 = 14x + -14x + -1x2 + x2 Combine like terms: 14x + -14x = 0 -44 + -13x + x2 = 0 + -1x2 + x2 -44 + -13x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -44 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -13x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -13x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -13x + x2 = 0 + 44 -13x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -13x + x2 = 44 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 44 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 44 + 42.25 Combine like terms: 44 + 42.25 = 86.25 42.25 + -13x + x2 = 86.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -6.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -6.5 = 9.287087811 Simplifying x + -6.5 = 9.287087811 Reorder the terms: -6.5 + x = 9.287087811 Solving -6.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 9.287087811 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 9.287087811 + 6.5 x = 9.287087811 + 6.5 Combine like terms: 9.287087811 + 6.5 = 15.787087811 x = 15.787087811 Simplifying x = 15.787087811Subproblem 2
x + -6.5 = -9.287087811 Simplifying x + -6.5 = -9.287087811 Reorder the terms: -6.5 + x = -9.287087811 Solving -6.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -9.287087811 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -9.287087811 + 6.5 x = -9.287087811 + 6.5 Combine like terms: -9.287087811 + 6.5 = -2.787087811 x = -2.787087811 Simplifying x = -2.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.787087811, -2.787087811}
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