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Simplifying x2 + 2x = 3969 Reorder the terms: 2x + x2 = 3969 Solving 2x + x2 = 3969 Solving for variable 'x'. Reorder the terms: -3969 + 2x + x2 = 3969 + -3969 Combine like terms: 3969 + -3969 = 0 -3969 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3969' to each side of the equation. -3969 + 2x + 3969 + x2 = 0 + 3969 Reorder the terms: -3969 + 3969 + 2x + x2 = 0 + 3969 Combine like terms: -3969 + 3969 = 0 0 + 2x + x2 = 0 + 3969 2x + x2 = 0 + 3969 Combine like terms: 0 + 3969 = 3969 2x + x2 = 3969 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 3969 + 1 Reorder the terms: 1 + 2x + x2 = 3969 + 1 Combine like terms: 3969 + 1 = 3970 1 + 2x + x2 = 3970 Factor a perfect square on the left side: (x + 1)(x + 1) = 3970 Calculate the square root of the right side: 63.007936008 Break this problem into two subproblems by setting (x + 1) equal to 63.007936008 and -63.007936008.Subproblem 1
x + 1 = 63.007936008 Simplifying x + 1 = 63.007936008 Reorder the terms: 1 + x = 63.007936008 Solving 1 + x = 63.007936008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 63.007936008 + -1 Combine like terms: 1 + -1 = 0 0 + x = 63.007936008 + -1 x = 63.007936008 + -1 Combine like terms: 63.007936008 + -1 = 62.007936008 x = 62.007936008 Simplifying x = 62.007936008Subproblem 2
x + 1 = -63.007936008 Simplifying x + 1 = -63.007936008 Reorder the terms: 1 + x = -63.007936008 Solving 1 + x = -63.007936008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -63.007936008 + -1 Combine like terms: 1 + -1 = 0 0 + x = -63.007936008 + -1 x = -63.007936008 + -1 Combine like terms: -63.007936008 + -1 = -64.007936008 x = -64.007936008 Simplifying x = -64.007936008Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.007936008, -64.007936008}
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