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Simplifying 2x2 + -9.5x + 5 = 0 Reorder the terms: 5 + -9.5x + 2x2 = 0 Solving 5 + -9.5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -4.75x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -4.75x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -4.75x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -4.75x + x2 = 0 + -2.5 -4.75x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -4.75x + x2 = -2.5 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = -2.5 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = -2.5 + 5.640625 Combine like terms: -2.5 + 5.640625 = 3.140625 5.640625 + -4.75x + x2 = 3.140625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + -2.375) equal to 1.77218086 and -1.77218086.Subproblem 1
x + -2.375 = 1.77218086 Simplifying x + -2.375 = 1.77218086 Reorder the terms: -2.375 + x = 1.77218086 Solving -2.375 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 1.77218086 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 1.77218086 + 2.375 x = 1.77218086 + 2.375 Combine like terms: 1.77218086 + 2.375 = 4.14718086 x = 4.14718086 Simplifying x = 4.14718086Subproblem 2
x + -2.375 = -1.77218086 Simplifying x + -2.375 = -1.77218086 Reorder the terms: -2.375 + x = -1.77218086 Solving -2.375 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -1.77218086 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -1.77218086 + 2.375 x = -1.77218086 + 2.375 Combine like terms: -1.77218086 + 2.375 = 0.60281914 x = 0.60281914 Simplifying x = 0.60281914Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.14718086, 0.60281914}
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