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Simplifying 4x2 + 27x + -44 = 0 Reorder the terms: -44 + 27x + 4x2 = 0 Solving -44 + 27x + 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 + 6.75x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 6.75x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 6.75x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6.75x + x2 = 0 + 11 6.75x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 6.75x + x2 = 11 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = 11 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = 11 + 11.390625 Combine like terms: 11 + 11.390625 = 22.390625 11.390625 + 6.75x + x2 = 22.390625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 22.390625 Calculate the square root of the right side: 4.731873308 Break this problem into two subproblems by setting (x + 3.375) equal to 4.731873308 and -4.731873308.Subproblem 1
x + 3.375 = 4.731873308 Simplifying x + 3.375 = 4.731873308 Reorder the terms: 3.375 + x = 4.731873308 Solving 3.375 + x = 4.731873308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 4.731873308 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 4.731873308 + -3.375 x = 4.731873308 + -3.375 Combine like terms: 4.731873308 + -3.375 = 1.356873308 x = 1.356873308 Simplifying x = 1.356873308Subproblem 2
x + 3.375 = -4.731873308 Simplifying x + 3.375 = -4.731873308 Reorder the terms: 3.375 + x = -4.731873308 Solving 3.375 + x = -4.731873308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -4.731873308 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -4.731873308 + -3.375 x = -4.731873308 + -3.375 Combine like terms: -4.731873308 + -3.375 = -8.106873308 x = -8.106873308 Simplifying x = -8.106873308Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.356873308, -8.106873308}
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