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Simplifying 4x2 + 35x + 9 = 0 Reorder the terms: 9 + 35x + 4x2 = 0 Solving 9 + 35x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 8.75x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 8.75x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 8.75x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 8.75x + x2 = 0 + -2.25 8.75x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 8.75x + x2 = -2.25 The x term is 8.75x. Take half its coefficient (4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. 8.75x + 19.140625 + x2 = -2.25 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = -2.25 + 19.140625 Combine like terms: -2.25 + 19.140625 = 16.890625 19.140625 + 8.75x + x2 = 16.890625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 16.890625 Calculate the square root of the right side: 4.109820556 Break this problem into two subproblems by setting (x + 4.375) equal to 4.109820556 and -4.109820556.Subproblem 1
x + 4.375 = 4.109820556 Simplifying x + 4.375 = 4.109820556 Reorder the terms: 4.375 + x = 4.109820556 Solving 4.375 + x = 4.109820556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = 4.109820556 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 4.109820556 + -4.375 x = 4.109820556 + -4.375 Combine like terms: 4.109820556 + -4.375 = -0.265179444 x = -0.265179444 Simplifying x = -0.265179444Subproblem 2
x + 4.375 = -4.109820556 Simplifying x + 4.375 = -4.109820556 Reorder the terms: 4.375 + x = -4.109820556 Solving 4.375 + x = -4.109820556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = -4.109820556 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -4.109820556 + -4.375 x = -4.109820556 + -4.375 Combine like terms: -4.109820556 + -4.375 = -8.484820556 x = -8.484820556 Simplifying x = -8.484820556Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.265179444, -8.484820556}
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