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Simplifying x2 + 100x + 80 = 0 Reorder the terms: 80 + 100x + x2 = 0 Solving 80 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 100x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + 100x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 100x + x2 = 0 + -80 100x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 100x + x2 = -80 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = -80 + 2500 Reorder the terms: 2500 + 100x + x2 = -80 + 2500 Combine like terms: -80 + 2500 = 2420 2500 + 100x + x2 = 2420 Factor a perfect square on the left side: (x + 50)(x + 50) = 2420 Calculate the square root of the right side: 49.193495505 Break this problem into two subproblems by setting (x + 50) equal to 49.193495505 and -49.193495505.Subproblem 1
x + 50 = 49.193495505 Simplifying x + 50 = 49.193495505 Reorder the terms: 50 + x = 49.193495505 Solving 50 + x = 49.193495505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 49.193495505 + -50 Combine like terms: 50 + -50 = 0 0 + x = 49.193495505 + -50 x = 49.193495505 + -50 Combine like terms: 49.193495505 + -50 = -0.806504495 x = -0.806504495 Simplifying x = -0.806504495Subproblem 2
x + 50 = -49.193495505 Simplifying x + 50 = -49.193495505 Reorder the terms: 50 + x = -49.193495505 Solving 50 + x = -49.193495505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -49.193495505 + -50 Combine like terms: 50 + -50 = 0 0 + x = -49.193495505 + -50 x = -49.193495505 + -50 Combine like terms: -49.193495505 + -50 = -99.193495505 x = -99.193495505 Simplifying x = -99.193495505Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.806504495, -99.193495505}
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