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Simplifying 112100 = -1x2 + -800x Reorder the terms: 112100 = -800x + -1x2 Solving 112100 = -800x + -1x2 Solving for variable 'x'. Reorder the terms: 112100 + 800x + x2 = -800x + 800x + -1x2 + x2 Combine like terms: -800x + 800x = 0 112100 + 800x + x2 = 0 + -1x2 + x2 112100 + 800x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 112100 + 800x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-112100' to each side of the equation. 112100 + 800x + -112100 + x2 = 0 + -112100 Reorder the terms: 112100 + -112100 + 800x + x2 = 0 + -112100 Combine like terms: 112100 + -112100 = 0 0 + 800x + x2 = 0 + -112100 800x + x2 = 0 + -112100 Combine like terms: 0 + -112100 = -112100 800x + x2 = -112100 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 = -112100 + 160000 Reorder the terms: 160000 + 800x + x2 = -112100 + 160000 Combine like terms: -112100 + 160000 = 47900 160000 + 800x + x2 = 47900 Factor a perfect square on the left side: (x + 400)(x + 400) = 47900 Calculate the square root of the right side: 218.860686282 Break this problem into two subproblems by setting (x + 400) equal to 218.860686282 and -218.860686282.Subproblem 1
x + 400 = 218.860686282 Simplifying x + 400 = 218.860686282 Reorder the terms: 400 + x = 218.860686282 Solving 400 + x = 218.860686282 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 = 218.860686282 + -400 Combine like terms: 400 + -400 = 0 0 + x = 218.860686282 + -400 x = 218.860686282 + -400 Combine like terms: 218.860686282 + -400 = -181.139313718 x = -181.139313718 Simplifying x = -181.139313718Subproblem 2
x + 400 = -218.860686282 Simplifying x + 400 = -218.860686282 Reorder the terms: 400 + x = -218.860686282 Solving 400 + x = -218.860686282 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 = -218.860686282 + -400 Combine like terms: 400 + -400 = 0 0 + x = -218.860686282 + -400 x = -218.860686282 + -400 Combine like terms: -218.860686282 + -400 = -618.860686282 x = -618.860686282 Simplifying x = -618.860686282Solution
The solution to the problem is based on the solutions from the subproblems. x = {-181.139313718, -618.860686282}
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