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Simplifying x2 + -2x + -99 = 0.2 Reorder the terms: -99 + -2x + x2 = 0.2 Solving -99 + -2x + x2 = 0.2 Solving for variable 'x'. Reorder the terms: -99 + -0.2 + -2x + x2 = 0.2 + -0.2 Combine like terms: -99 + -0.2 = -99.2 -99.2 + -2x + x2 = 0.2 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 -99.2 + -2x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '99.2' to each side of the equation. -99.2 + -2x + 99.2 + x2 = 0.0 + 99.2 Reorder the terms: -99.2 + 99.2 + -2x + x2 = 0.0 + 99.2 Combine like terms: -99.2 + 99.2 = 0.0 0.0 + -2x + x2 = 0.0 + 99.2 -2x + x2 = 0.0 + 99.2 Combine like terms: 0.0 + 99.2 = 99.2 -2x + x2 = 99.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 99.2 + 1 Reorder the terms: 1 + -2x + x2 = 99.2 + 1 Combine like terms: 99.2 + 1 = 100.2 1 + -2x + x2 = 100.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 100.2 Calculate the square root of the right side: 10.009995005 Break this problem into two subproblems by setting (x + -1) equal to 10.009995005 and -10.009995005.Subproblem 1
x + -1 = 10.009995005 Simplifying x + -1 = 10.009995005 Reorder the terms: -1 + x = 10.009995005 Solving -1 + x = 10.009995005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.009995005 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.009995005 + 1 x = 10.009995005 + 1 Combine like terms: 10.009995005 + 1 = 11.009995005 x = 11.009995005 Simplifying x = 11.009995005Subproblem 2
x + -1 = -10.009995005 Simplifying x + -1 = -10.009995005 Reorder the terms: -1 + x = -10.009995005 Solving -1 + x = -10.009995005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.009995005 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.009995005 + 1 x = -10.009995005 + 1 Combine like terms: -10.009995005 + 1 = -9.009995005 x = -9.009995005 Simplifying x = -9.009995005Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.009995005, -9.009995005}
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