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Simplifying 4x2 + 35x + 44 = 0 Reorder the terms: 44 + 35x + 4x2 = 0 Solving 44 + 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'. 11 + 8.75x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + 8.75x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 8.75x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 8.75x + x2 = 0 + -11 8.75x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 8.75x + x2 = -11 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 = -11 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = -11 + 19.140625 Combine like terms: -11 + 19.140625 = 8.140625 19.140625 + 8.75x + x2 = 8.140625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 8.140625 Calculate the square root of the right side: 2.853178053 Break this problem into two subproblems by setting (x + 4.375) equal to 2.853178053 and -2.853178053.Subproblem 1
x + 4.375 = 2.853178053 Simplifying x + 4.375 = 2.853178053 Reorder the terms: 4.375 + x = 2.853178053 Solving 4.375 + x = 2.853178053 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 = 2.853178053 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 2.853178053 + -4.375 x = 2.853178053 + -4.375 Combine like terms: 2.853178053 + -4.375 = -1.521821947 x = -1.521821947 Simplifying x = -1.521821947Subproblem 2
x + 4.375 = -2.853178053 Simplifying x + 4.375 = -2.853178053 Reorder the terms: 4.375 + x = -2.853178053 Solving 4.375 + x = -2.853178053 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 = -2.853178053 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -2.853178053 + -4.375 x = -2.853178053 + -4.375 Combine like terms: -2.853178053 + -4.375 = -7.228178053 x = -7.228178053 Simplifying x = -7.228178053Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.521821947, -7.228178053}
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