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Simplifying x2 + 32x + 41 = 0 Reorder the terms: 41 + 32x + x2 = 0 Solving 41 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 32x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 32x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 32x + x2 = 0 + -41 32x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 32x + x2 = -41 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -41 + 256 Reorder the terms: 256 + 32x + x2 = -41 + 256 Combine like terms: -41 + 256 = 215 256 + 32x + x2 = 215 Factor a perfect square on the left side: (x + 16)(x + 16) = 215 Calculate the square root of the right side: 14.662878299 Break this problem into two subproblems by setting (x + 16) equal to 14.662878299 and -14.662878299.Subproblem 1
x + 16 = 14.662878299 Simplifying x + 16 = 14.662878299 Reorder the terms: 16 + x = 14.662878299 Solving 16 + x = 14.662878299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 14.662878299 + -16 Combine like terms: 16 + -16 = 0 0 + x = 14.662878299 + -16 x = 14.662878299 + -16 Combine like terms: 14.662878299 + -16 = -1.337121701 x = -1.337121701 Simplifying x = -1.337121701Subproblem 2
x + 16 = -14.662878299 Simplifying x + 16 = -14.662878299 Reorder the terms: 16 + x = -14.662878299 Solving 16 + x = -14.662878299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -14.662878299 + -16 Combine like terms: 16 + -16 = 0 0 + x = -14.662878299 + -16 x = -14.662878299 + -16 Combine like terms: -14.662878299 + -16 = -30.662878299 x = -30.662878299 Simplifying x = -30.662878299Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.337121701, -30.662878299}
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