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Simplifying 4.11x2 + -2.33x + -1.98 = 0 Reorder the terms: -1.98 + -2.33x + 4.11x2 = 0 Solving -1.98 + -2.33x + 4.11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.11 the coefficient of the squared term: Divide each side by '4.11'. -0.4817518248 + -0.5669099757x + x2 = 0 Move the constant term to the right: Add '0.4817518248' to each side of the equation. -0.4817518248 + -0.5669099757x + 0.4817518248 + x2 = 0 + 0.4817518248 Reorder the terms: -0.4817518248 + 0.4817518248 + -0.5669099757x + x2 = 0 + 0.4817518248 Combine like terms: -0.4817518248 + 0.4817518248 = 0.0000000000 0.0000000000 + -0.5669099757x + x2 = 0 + 0.4817518248 -0.5669099757x + x2 = 0 + 0.4817518248 Combine like terms: 0 + 0.4817518248 = 0.4817518248 -0.5669099757x + x2 = 0.4817518248 The x term is -0.5669099757x. Take half its coefficient (-0.2834549879). Square it (0.08034673017) and add it to both sides. Add '0.08034673017' to each side of the equation. -0.5669099757x + 0.08034673017 + x2 = 0.4817518248 + 0.08034673017 Reorder the terms: 0.08034673017 + -0.5669099757x + x2 = 0.4817518248 + 0.08034673017 Combine like terms: 0.4817518248 + 0.08034673017 = 0.56209855497 0.08034673017 + -0.5669099757x + x2 = 0.56209855497 Factor a perfect square on the left side: (x + -0.2834549879)(x + -0.2834549879) = 0.56209855497 Calculate the square root of the right side: 0.749732322 Break this problem into two subproblems by setting (x + -0.2834549879) equal to 0.749732322 and -0.749732322.Subproblem 1
x + -0.2834549879 = 0.749732322 Simplifying x + -0.2834549879 = 0.749732322 Reorder the terms: -0.2834549879 + x = 0.749732322 Solving -0.2834549879 + x = 0.749732322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2834549879' to each side of the equation. -0.2834549879 + 0.2834549879 + x = 0.749732322 + 0.2834549879 Combine like terms: -0.2834549879 + 0.2834549879 = 0.0000000000 0.0000000000 + x = 0.749732322 + 0.2834549879 x = 0.749732322 + 0.2834549879 Combine like terms: 0.749732322 + 0.2834549879 = 1.0331873099 x = 1.0331873099 Simplifying x = 1.0331873099Subproblem 2
x + -0.2834549879 = -0.749732322 Simplifying x + -0.2834549879 = -0.749732322 Reorder the terms: -0.2834549879 + x = -0.749732322 Solving -0.2834549879 + x = -0.749732322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2834549879' to each side of the equation. -0.2834549879 + 0.2834549879 + x = -0.749732322 + 0.2834549879 Combine like terms: -0.2834549879 + 0.2834549879 = 0.0000000000 0.0000000000 + x = -0.749732322 + 0.2834549879 x = -0.749732322 + 0.2834549879 Combine like terms: -0.749732322 + 0.2834549879 = -0.4662773341 x = -0.4662773341 Simplifying x = -0.4662773341Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0331873099, -0.4662773341}
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