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Simplifying 8.06x2 + 25.8726x + -25.047256 = 0 Reorder the terms: -25.047256 + 25.8726x + 8.06x2 = 0 Solving -25.047256 + 25.8726x + 8.06x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.06 the coefficient of the squared term: Divide each side by '8.06'. -3.1076 + 3.21x + x2 = 0 Move the constant term to the right: Add '3.1076' to each side of the equation. -3.1076 + 3.21x + 3.1076 + x2 = 0 + 3.1076 Reorder the terms: -3.1076 + 3.1076 + 3.21x + x2 = 0 + 3.1076 Combine like terms: -3.1076 + 3.1076 = 0.0000 0.0000 + 3.21x + x2 = 0 + 3.1076 3.21x + x2 = 0 + 3.1076 Combine like terms: 0 + 3.1076 = 3.1076 3.21x + x2 = 3.1076 The x term is 3.21x. Take half its coefficient (1.605). Square it (2.576025) and add it to both sides. Add '2.576025' to each side of the equation. 3.21x + 2.576025 + x2 = 3.1076 + 2.576025 Reorder the terms: 2.576025 + 3.21x + x2 = 3.1076 + 2.576025 Combine like terms: 3.1076 + 2.576025 = 5.683625 2.576025 + 3.21x + x2 = 5.683625 Factor a perfect square on the left side: (x + 1.605)(x + 1.605) = 5.683625 Calculate the square root of the right side: 2.384035444 Break this problem into two subproblems by setting (x + 1.605) equal to 2.384035444 and -2.384035444.Subproblem 1
x + 1.605 = 2.384035444 Simplifying x + 1.605 = 2.384035444 Reorder the terms: 1.605 + x = 2.384035444 Solving 1.605 + x = 2.384035444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.605' to each side of the equation. 1.605 + -1.605 + x = 2.384035444 + -1.605 Combine like terms: 1.605 + -1.605 = 0.000 0.000 + x = 2.384035444 + -1.605 x = 2.384035444 + -1.605 Combine like terms: 2.384035444 + -1.605 = 0.779035444 x = 0.779035444 Simplifying x = 0.779035444Subproblem 2
x + 1.605 = -2.384035444 Simplifying x + 1.605 = -2.384035444 Reorder the terms: 1.605 + x = -2.384035444 Solving 1.605 + x = -2.384035444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.605' to each side of the equation. 1.605 + -1.605 + x = -2.384035444 + -1.605 Combine like terms: 1.605 + -1.605 = 0.000 0.000 + x = -2.384035444 + -1.605 x = -2.384035444 + -1.605 Combine like terms: -2.384035444 + -1.605 = -3.989035444 x = -3.989035444 Simplifying x = -3.989035444Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.779035444, -3.989035444}
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