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Simplifying 99x2 + 20x + -200 = 0 Reorder the terms: -200 + 20x + 99x2 = 0 Solving -200 + 20x + 99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. -2.02020202 + 0.202020202x + x2 = 0 Move the constant term to the right: Add '2.02020202' to each side of the equation. -2.02020202 + 0.202020202x + 2.02020202 + x2 = 0 + 2.02020202 Reorder the terms: -2.02020202 + 2.02020202 + 0.202020202x + x2 = 0 + 2.02020202 Combine like terms: -2.02020202 + 2.02020202 = 0.00000000 0.00000000 + 0.202020202x + x2 = 0 + 2.02020202 0.202020202x + x2 = 0 + 2.02020202 Combine like terms: 0 + 2.02020202 = 2.02020202 0.202020202x + x2 = 2.02020202 The x term is 0.202020202x. Take half its coefficient (0.101010101). Square it (0.01020304050) and add it to both sides. Add '0.01020304050' to each side of the equation. 0.202020202x + 0.01020304050 + x2 = 2.02020202 + 0.01020304050 Reorder the terms: 0.01020304050 + 0.202020202x + x2 = 2.02020202 + 0.01020304050 Combine like terms: 2.02020202 + 0.01020304050 = 2.0304050605 0.01020304050 + 0.202020202x + x2 = 2.0304050605 Factor a perfect square on the left side: (x + 0.101010101)(x + 0.101010101) = 2.0304050605 Calculate the square root of the right side: 1.424922826 Break this problem into two subproblems by setting (x + 0.101010101) equal to 1.424922826 and -1.424922826.Subproblem 1
x + 0.101010101 = 1.424922826 Simplifying x + 0.101010101 = 1.424922826 Reorder the terms: 0.101010101 + x = 1.424922826 Solving 0.101010101 + x = 1.424922826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.101010101' to each side of the equation. 0.101010101 + -0.101010101 + x = 1.424922826 + -0.101010101 Combine like terms: 0.101010101 + -0.101010101 = 0.000000000 0.000000000 + x = 1.424922826 + -0.101010101 x = 1.424922826 + -0.101010101 Combine like terms: 1.424922826 + -0.101010101 = 1.323912725 x = 1.323912725 Simplifying x = 1.323912725Subproblem 2
x + 0.101010101 = -1.424922826 Simplifying x + 0.101010101 = -1.424922826 Reorder the terms: 0.101010101 + x = -1.424922826 Solving 0.101010101 + x = -1.424922826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.101010101' to each side of the equation. 0.101010101 + -0.101010101 + x = -1.424922826 + -0.101010101 Combine like terms: 0.101010101 + -0.101010101 = 0.000000000 0.000000000 + x = -1.424922826 + -0.101010101 x = -1.424922826 + -0.101010101 Combine like terms: -1.424922826 + -0.101010101 = -1.525932927 x = -1.525932927 Simplifying x = -1.525932927Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.323912725, -1.525932927}
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