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Simplifying x2 + 4x = 4196 Reorder the terms: 4x + x2 = 4196 Solving 4x + x2 = 4196 Solving for variable 'x'. Reorder the terms: -4196 + 4x + x2 = 4196 + -4196 Combine like terms: 4196 + -4196 = 0 -4196 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4196' to each side of the equation. -4196 + 4x + 4196 + x2 = 0 + 4196 Reorder the terms: -4196 + 4196 + 4x + x2 = 0 + 4196 Combine like terms: -4196 + 4196 = 0 0 + 4x + x2 = 0 + 4196 4x + x2 = 0 + 4196 Combine like terms: 0 + 4196 = 4196 4x + x2 = 4196 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 4196 + 4 Reorder the terms: 4 + 4x + x2 = 4196 + 4 Combine like terms: 4196 + 4 = 4200 4 + 4x + x2 = 4200 Factor a perfect square on the left side: (x + 2)(x + 2) = 4200 Calculate the square root of the right side: 64.807406984 Break this problem into two subproblems by setting (x + 2) equal to 64.807406984 and -64.807406984.Subproblem 1
x + 2 = 64.807406984 Simplifying x + 2 = 64.807406984 Reorder the terms: 2 + x = 64.807406984 Solving 2 + x = 64.807406984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 64.807406984 + -2 Combine like terms: 2 + -2 = 0 0 + x = 64.807406984 + -2 x = 64.807406984 + -2 Combine like terms: 64.807406984 + -2 = 62.807406984 x = 62.807406984 Simplifying x = 62.807406984Subproblem 2
x + 2 = -64.807406984 Simplifying x + 2 = -64.807406984 Reorder the terms: 2 + x = -64.807406984 Solving 2 + x = -64.807406984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -64.807406984 + -2 Combine like terms: 2 + -2 = 0 0 + x = -64.807406984 + -2 x = -64.807406984 + -2 Combine like terms: -64.807406984 + -2 = -66.807406984 x = -66.807406984 Simplifying x = -66.807406984Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.807406984, -66.807406984}
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