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Simplifying -20x2 + 10x + 1 = 0 Reorder the terms: 1 + 10x + -20x2 = 0 Solving 1 + 10x + -20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.05 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + -0.5x + 0.05 + x2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + -0.5x + x2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + -0.5x + x2 = 0 + 0.05 -0.5x + x2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 -0.5x + x2 = 0.05 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.05 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.05 + 0.0625 Combine like terms: 0.05 + 0.0625 = 0.1125 0.0625 + -0.5x + x2 = 0.1125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.1125 Calculate the square root of the right side: 0.335410197 Break this problem into two subproblems by setting (x + -0.25) equal to 0.335410197 and -0.335410197.Subproblem 1
x + -0.25 = 0.335410197 Simplifying x + -0.25 = 0.335410197 Reorder the terms: -0.25 + x = 0.335410197 Solving -0.25 + x = 0.335410197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.335410197 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.335410197 + 0.25 x = 0.335410197 + 0.25 Combine like terms: 0.335410197 + 0.25 = 0.585410197 x = 0.585410197 Simplifying x = 0.585410197Subproblem 2
x + -0.25 = -0.335410197 Simplifying x + -0.25 = -0.335410197 Reorder the terms: -0.25 + x = -0.335410197 Solving -0.25 + x = -0.335410197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.335410197 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.335410197 + 0.25 x = -0.335410197 + 0.25 Combine like terms: -0.335410197 + 0.25 = -0.085410197 x = -0.085410197 Simplifying x = -0.085410197Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.585410197, -0.085410197}
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