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Simplifying -1x2 + -0.822x + 0.182 = 0 Reorder the terms: 0.182 + -0.822x + -1x2 = 0 Solving 0.182 + -0.822x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.182 + 0.822x + x2 = 0 Move the constant term to the right: Add '0.182' to each side of the equation. -0.182 + 0.822x + 0.182 + x2 = 0 + 0.182 Reorder the terms: -0.182 + 0.182 + 0.822x + x2 = 0 + 0.182 Combine like terms: -0.182 + 0.182 = 0.000 0.000 + 0.822x + x2 = 0 + 0.182 0.822x + x2 = 0 + 0.182 Combine like terms: 0 + 0.182 = 0.182 0.822x + x2 = 0.182 The x term is 0.822x. Take half its coefficient (0.411). Square it (0.168921) and add it to both sides. Add '0.168921' to each side of the equation. 0.822x + 0.168921 + x2 = 0.182 + 0.168921 Reorder the terms: 0.168921 + 0.822x + x2 = 0.182 + 0.168921 Combine like terms: 0.182 + 0.168921 = 0.350921 0.168921 + 0.822x + x2 = 0.350921 Factor a perfect square on the left side: (x + 0.411)(x + 0.411) = 0.350921 Calculate the square root of the right side: 0.592385854 Break this problem into two subproblems by setting (x + 0.411) equal to 0.592385854 and -0.592385854.Subproblem 1
x + 0.411 = 0.592385854 Simplifying x + 0.411 = 0.592385854 Reorder the terms: 0.411 + x = 0.592385854 Solving 0.411 + x = 0.592385854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.411' to each side of the equation. 0.411 + -0.411 + x = 0.592385854 + -0.411 Combine like terms: 0.411 + -0.411 = 0.000 0.000 + x = 0.592385854 + -0.411 x = 0.592385854 + -0.411 Combine like terms: 0.592385854 + -0.411 = 0.181385854 x = 0.181385854 Simplifying x = 0.181385854Subproblem 2
x + 0.411 = -0.592385854 Simplifying x + 0.411 = -0.592385854 Reorder the terms: 0.411 + x = -0.592385854 Solving 0.411 + x = -0.592385854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.411' to each side of the equation. 0.411 + -0.411 + x = -0.592385854 + -0.411 Combine like terms: 0.411 + -0.411 = 0.000 0.000 + x = -0.592385854 + -0.411 x = -0.592385854 + -0.411 Combine like terms: -0.592385854 + -0.411 = -1.003385854 x = -1.003385854 Simplifying x = -1.003385854Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.181385854, -1.003385854}
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