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Simplifying x2 + 41x + -640 = 0 Reorder the terms: -640 + 41x + x2 = 0 Solving -640 + 41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '640' to each side of the equation. -640 + 41x + 640 + x2 = 0 + 640 Reorder the terms: -640 + 640 + 41x + x2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + 41x + x2 = 0 + 640 41x + x2 = 0 + 640 Combine like terms: 0 + 640 = 640 41x + x2 = 640 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = 640 + 420.25 Reorder the terms: 420.25 + 41x + x2 = 640 + 420.25 Combine like terms: 640 + 420.25 = 1060.25 420.25 + 41x + x2 = 1060.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 1060.25 Calculate the square root of the right side: 32.56148031 Break this problem into two subproblems by setting (x + 20.5) equal to 32.56148031 and -32.56148031.Subproblem 1
x + 20.5 = 32.56148031 Simplifying x + 20.5 = 32.56148031 Reorder the terms: 20.5 + x = 32.56148031 Solving 20.5 + x = 32.56148031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 32.56148031 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 32.56148031 + -20.5 x = 32.56148031 + -20.5 Combine like terms: 32.56148031 + -20.5 = 12.06148031 x = 12.06148031 Simplifying x = 12.06148031Subproblem 2
x + 20.5 = -32.56148031 Simplifying x + 20.5 = -32.56148031 Reorder the terms: 20.5 + x = -32.56148031 Solving 20.5 + x = -32.56148031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -32.56148031 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -32.56148031 + -20.5 x = -32.56148031 + -20.5 Combine like terms: -32.56148031 + -20.5 = -53.06148031 x = -53.06148031 Simplifying x = -53.06148031Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.06148031, -53.06148031}
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