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Simplifying 100x2 + -99x + -99 = 0 Reorder the terms: -99 + -99x + 100x2 = 0 Solving -99 + -99x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.99 + -0.99x + x2 = 0 Move the constant term to the right: Add '0.99' to each side of the equation. -0.99 + -0.99x + 0.99 + x2 = 0 + 0.99 Reorder the terms: -0.99 + 0.99 + -0.99x + x2 = 0 + 0.99 Combine like terms: -0.99 + 0.99 = 0.00 0.00 + -0.99x + x2 = 0 + 0.99 -0.99x + x2 = 0 + 0.99 Combine like terms: 0 + 0.99 = 0.99 -0.99x + x2 = 0.99 The x term is -0.99x. Take half its coefficient (-0.495). Square it (0.245025) and add it to both sides. Add '0.245025' to each side of the equation. -0.99x + 0.245025 + x2 = 0.99 + 0.245025 Reorder the terms: 0.245025 + -0.99x + x2 = 0.99 + 0.245025 Combine like terms: 0.99 + 0.245025 = 1.235025 0.245025 + -0.99x + x2 = 1.235025 Factor a perfect square on the left side: (x + -0.495)(x + -0.495) = 1.235025 Calculate the square root of the right side: 1.111316787 Break this problem into two subproblems by setting (x + -0.495) equal to 1.111316787 and -1.111316787.Subproblem 1
x + -0.495 = 1.111316787 Simplifying x + -0.495 = 1.111316787 Reorder the terms: -0.495 + x = 1.111316787 Solving -0.495 + x = 1.111316787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.495' to each side of the equation. -0.495 + 0.495 + x = 1.111316787 + 0.495 Combine like terms: -0.495 + 0.495 = 0.000 0.000 + x = 1.111316787 + 0.495 x = 1.111316787 + 0.495 Combine like terms: 1.111316787 + 0.495 = 1.606316787 x = 1.606316787 Simplifying x = 1.606316787Subproblem 2
x + -0.495 = -1.111316787 Simplifying x + -0.495 = -1.111316787 Reorder the terms: -0.495 + x = -1.111316787 Solving -0.495 + x = -1.111316787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.495' to each side of the equation. -0.495 + 0.495 + x = -1.111316787 + 0.495 Combine like terms: -0.495 + 0.495 = 0.000 0.000 + x = -1.111316787 + 0.495 x = -1.111316787 + 0.495 Combine like terms: -1.111316787 + 0.495 = -0.616316787 x = -0.616316787 Simplifying x = -0.616316787Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.606316787, -0.616316787}
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