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Simplifying x2 + -80x + -500 = 0 Reorder the terms: -500 + -80x + x2 = 0 Solving -500 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + -80x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -80x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -80x + x2 = 0 + 500 -80x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -80x + x2 = 500 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 500 + 1600 Reorder the terms: 1600 + -80x + x2 = 500 + 1600 Combine like terms: 500 + 1600 = 2100 1600 + -80x + x2 = 2100 Factor a perfect square on the left side: (x + -40)(x + -40) = 2100 Calculate the square root of the right side: 45.82575695 Break this problem into two subproblems by setting (x + -40) equal to 45.82575695 and -45.82575695.Subproblem 1
x + -40 = 45.82575695 Simplifying x + -40 = 45.82575695 Reorder the terms: -40 + x = 45.82575695 Solving -40 + x = 45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 45.82575695 + 40 Combine like terms: -40 + 40 = 0 0 + x = 45.82575695 + 40 x = 45.82575695 + 40 Combine like terms: 45.82575695 + 40 = 85.82575695 x = 85.82575695 Simplifying x = 85.82575695Subproblem 2
x + -40 = -45.82575695 Simplifying x + -40 = -45.82575695 Reorder the terms: -40 + x = -45.82575695 Solving -40 + x = -45.82575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -45.82575695 + 40 Combine like terms: -40 + 40 = 0 0 + x = -45.82575695 + 40 x = -45.82575695 + 40 Combine like terms: -45.82575695 + 40 = -5.82575695 x = -5.82575695 Simplifying x = -5.82575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {85.82575695, -5.82575695}
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