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Simplifying 100x2 + -11x + -6 = 0 Reorder the terms: -6 + -11x + 100x2 = 0 Solving -6 + -11x + 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'. -0.06 + -0.11x + x2 = 0 Move the constant term to the right: Add '0.06' to each side of the equation. -0.06 + -0.11x + 0.06 + x2 = 0 + 0.06 Reorder the terms: -0.06 + 0.06 + -0.11x + x2 = 0 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + -0.11x + x2 = 0 + 0.06 -0.11x + x2 = 0 + 0.06 Combine like terms: 0 + 0.06 = 0.06 -0.11x + x2 = 0.06 The x term is -0.11x. Take half its coefficient (-0.055). Square it (0.003025) and add it to both sides. Add '0.003025' to each side of the equation. -0.11x + 0.003025 + x2 = 0.06 + 0.003025 Reorder the terms: 0.003025 + -0.11x + x2 = 0.06 + 0.003025 Combine like terms: 0.06 + 0.003025 = 0.063025 0.003025 + -0.11x + x2 = 0.063025 Factor a perfect square on the left side: (x + -0.055)(x + -0.055) = 0.063025 Calculate the square root of the right side: 0.251047804 Break this problem into two subproblems by setting (x + -0.055) equal to 0.251047804 and -0.251047804.Subproblem 1
x + -0.055 = 0.251047804 Simplifying x + -0.055 = 0.251047804 Reorder the terms: -0.055 + x = 0.251047804 Solving -0.055 + x = 0.251047804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.055' to each side of the equation. -0.055 + 0.055 + x = 0.251047804 + 0.055 Combine like terms: -0.055 + 0.055 = 0.000 0.000 + x = 0.251047804 + 0.055 x = 0.251047804 + 0.055 Combine like terms: 0.251047804 + 0.055 = 0.306047804 x = 0.306047804 Simplifying x = 0.306047804Subproblem 2
x + -0.055 = -0.251047804 Simplifying x + -0.055 = -0.251047804 Reorder the terms: -0.055 + x = -0.251047804 Solving -0.055 + x = -0.251047804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.055' to each side of the equation. -0.055 + 0.055 + x = -0.251047804 + 0.055 Combine like terms: -0.055 + 0.055 = 0.000 0.000 + x = -0.251047804 + 0.055 x = -0.251047804 + 0.055 Combine like terms: -0.251047804 + 0.055 = -0.196047804 x = -0.196047804 Simplifying x = -0.196047804Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.306047804, -0.196047804}
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