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Simplifying x2 + -800x + 20000 = 0 Reorder the terms: 20000 + -800x + x2 = 0 Solving 20000 + -800x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20000' to each side of the equation. 20000 + -800x + -20000 + x2 = 0 + -20000 Reorder the terms: 20000 + -20000 + -800x + x2 = 0 + -20000 Combine like terms: 20000 + -20000 = 0 0 + -800x + x2 = 0 + -20000 -800x + x2 = 0 + -20000 Combine like terms: 0 + -20000 = -20000 -800x + x2 = -20000 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = -20000 + 160000 Reorder the terms: 160000 + -800x + x2 = -20000 + 160000 Combine like terms: -20000 + 160000 = 140000 160000 + -800x + x2 = 140000 Factor a perfect square on the left side: (x + -400)(x + -400) = 140000 Calculate the square root of the right side: 374.165738677 Break this problem into two subproblems by setting (x + -400) equal to 374.165738677 and -374.165738677.Subproblem 1
x + -400 = 374.165738677 Simplifying x + -400 = 374.165738677 Reorder the terms: -400 + x = 374.165738677 Solving -400 + x = 374.165738677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 374.165738677 + 400 Combine like terms: -400 + 400 = 0 0 + x = 374.165738677 + 400 x = 374.165738677 + 400 Combine like terms: 374.165738677 + 400 = 774.165738677 x = 774.165738677 Simplifying x = 774.165738677Subproblem 2
x + -400 = -374.165738677 Simplifying x + -400 = -374.165738677 Reorder the terms: -400 + x = -374.165738677 Solving -400 + x = -374.165738677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -374.165738677 + 400 Combine like terms: -400 + 400 = 0 0 + x = -374.165738677 + 400 x = -374.165738677 + 400 Combine like terms: -374.165738677 + 400 = 25.834261323 x = 25.834261323 Simplifying x = 25.834261323Solution
The solution to the problem is based on the solutions from the subproblems. x = {774.165738677, 25.834261323}
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