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Simplifying 100x2 + -1x + -10 = 0 Reorder the terms: -10 + -1x + 100x2 = 0 Solving -10 + -1x + 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'. -0.1 + -0.01x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.01x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.01x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.01x + x2 = 0 + 0.1 -0.01x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -0.01x + x2 = 0.1 The x term is -0.01x. Take half its coefficient (-0.005). Square it (0.000025) and add it to both sides. Add '0.000025' to each side of the equation. -0.01x + 0.000025 + x2 = 0.1 + 0.000025 Reorder the terms: 0.000025 + -0.01x + x2 = 0.1 + 0.000025 Combine like terms: 0.1 + 0.000025 = 0.100025 0.000025 + -0.01x + x2 = 0.100025 Factor a perfect square on the left side: (x + -0.005)(x + -0.005) = 0.100025 Calculate the square root of the right side: 0.316267292 Break this problem into two subproblems by setting (x + -0.005) equal to 0.316267292 and -0.316267292.Subproblem 1
x + -0.005 = 0.316267292 Simplifying x + -0.005 = 0.316267292 Reorder the terms: -0.005 + x = 0.316267292 Solving -0.005 + x = 0.316267292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005' to each side of the equation. -0.005 + 0.005 + x = 0.316267292 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = 0.316267292 + 0.005 x = 0.316267292 + 0.005 Combine like terms: 0.316267292 + 0.005 = 0.321267292 x = 0.321267292 Simplifying x = 0.321267292Subproblem 2
x + -0.005 = -0.316267292 Simplifying x + -0.005 = -0.316267292 Reorder the terms: -0.005 + x = -0.316267292 Solving -0.005 + x = -0.316267292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005' to each side of the equation. -0.005 + 0.005 + x = -0.316267292 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = -0.316267292 + 0.005 x = -0.316267292 + 0.005 Combine like terms: -0.316267292 + 0.005 = -0.311267292 x = -0.311267292 Simplifying x = -0.311267292Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.321267292, -0.311267292}
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