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Simplifying 2x2 + 9.5x + -9.5 = 0 Reorder the terms: -9.5 + 9.5x + 2x2 = 0 Solving -9.5 + 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'. -4.75 + 4.75x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 4.75x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 4.75x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 4.75x + x2 = 0 + 4.75 4.75x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 4.75x + x2 = 4.75 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 = 4.75 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 4.75 + 5.640625 Combine like terms: 4.75 + 5.640625 = 10.390625 5.640625 + 4.75x + x2 = 10.390625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 10.390625 Calculate the square root of the right side: 3.22344924 Break this problem into two subproblems by setting (x + 2.375) equal to 3.22344924 and -3.22344924.Subproblem 1
x + 2.375 = 3.22344924 Simplifying x + 2.375 = 3.22344924 Reorder the terms: 2.375 + x = 3.22344924 Solving 2.375 + x = 3.22344924 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 = 3.22344924 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 3.22344924 + -2.375 x = 3.22344924 + -2.375 Combine like terms: 3.22344924 + -2.375 = 0.84844924 x = 0.84844924 Simplifying x = 0.84844924Subproblem 2
x + 2.375 = -3.22344924 Simplifying x + 2.375 = -3.22344924 Reorder the terms: 2.375 + x = -3.22344924 Solving 2.375 + x = -3.22344924 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 = -3.22344924 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -3.22344924 + -2.375 x = -3.22344924 + -2.375 Combine like terms: -3.22344924 + -2.375 = -5.59844924 x = -5.59844924 Simplifying x = -5.59844924Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.84844924, -5.59844924}
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