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Simplifying x2 + -80x = -200 Reorder the terms: -80x + x2 = -200 Solving -80x + x2 = -200 Solving for variable 'x'. Reorder the terms: 200 + -80x + x2 = -200 + 200 Combine like terms: -200 + 200 = 0 200 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -80x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -80x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -80x + x2 = 0 + -200 -80x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -80x + x2 = -200 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 = -200 + 1600 Reorder the terms: 1600 + -80x + x2 = -200 + 1600 Combine like terms: -200 + 1600 = 1400 1600 + -80x + x2 = 1400 Factor a perfect square on the left side: (x + -40)(x + -40) = 1400 Calculate the square root of the right side: 37.416573868 Break this problem into two subproblems by setting (x + -40) equal to 37.416573868 and -37.416573868.Subproblem 1
x + -40 = 37.416573868 Simplifying x + -40 = 37.416573868 Reorder the terms: -40 + x = 37.416573868 Solving -40 + x = 37.416573868 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 = 37.416573868 + 40 Combine like terms: -40 + 40 = 0 0 + x = 37.416573868 + 40 x = 37.416573868 + 40 Combine like terms: 37.416573868 + 40 = 77.416573868 x = 77.416573868 Simplifying x = 77.416573868Subproblem 2
x + -40 = -37.416573868 Simplifying x + -40 = -37.416573868 Reorder the terms: -40 + x = -37.416573868 Solving -40 + x = -37.416573868 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 = -37.416573868 + 40 Combine like terms: -40 + 40 = 0 0 + x = -37.416573868 + 40 x = -37.416573868 + 40 Combine like terms: -37.416573868 + 40 = 2.583426132 x = 2.583426132 Simplifying x = 2.583426132Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.416573868, 2.583426132}
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