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Simplifying (0.4x2) + -1.1x = 2 Reorder the terms: -1.1x + (0.4x2) = 2 Solving -1.1x + (0.4x2) = 2 Solving for variable 'x'. Reorder the terms: -2 + -1.1x + (0.4x2) = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -1.1x + (0.4x2) = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -5 + -2.75x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.75x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2.75x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.75x + x2 = 0 + 5 -2.75x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.75x + x2 = 5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 5 + 1.890625 Combine like terms: 5 + 1.890625 = 6.890625 1.890625 + -2.75x + x2 = 6.890625 Factor a perfect square on the left side: ((x) + -1.375)((x) + -1.375) = 6.890625 Calculate the square root of the right side: 2.625 Break this problem into two subproblems by setting ((x) + -1.375) equal to 2.625 and -2.625.Subproblem 1
(x) + -1.375 = 2.625 Simplifying (x) + -1.375 = 2.625 x + -1.375 = 2.625 Reorder the terms: -1.375 + x = 2.625 Solving -1.375 + x = 2.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.625 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.625 + 1.375 x = 2.625 + 1.375 Combine like terms: 2.625 + 1.375 = 4 x = 4 Simplifying x = 4Subproblem 2
(x) + -1.375 = -2.625 Simplifying (x) + -1.375 = -2.625 x + -1.375 = -2.625 Reorder the terms: -1.375 + x = -2.625 Solving -1.375 + x = -2.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.625 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.625 + 1.375 x = -2.625 + 1.375 Combine like terms: -2.625 + 1.375 = -1.25 x = -1.25 Simplifying x = -1.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -1.25}
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