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Simplifying 3X + 9 = -2X(2X) + 44 Reorder the terms: 9 + 3X = -2X(2X) + 44 Remove parenthesis around (2X) 9 + 3X = -2X * 2X + 44 Reorder the terms for easier multiplication: 9 + 3X = -2 * 2X * X + 44 Multiply -2 * 2 9 + 3X = -4X * X + 44 Multiply X * X 9 + 3X = -4X2 + 44 Reorder the terms: 9 + 3X = 44 + -4X2 Solving 9 + 3X = 44 + -4X2 Solving for variable 'X'. Reorder the terms: 9 + -44 + 3X + 4X2 = 44 + -4X2 + -44 + 4X2 Combine like terms: 9 + -44 = -35 -35 + 3X + 4X2 = 44 + -4X2 + -44 + 4X2 Reorder the terms: -35 + 3X + 4X2 = 44 + -44 + -4X2 + 4X2 Combine like terms: 44 + -44 = 0 -35 + 3X + 4X2 = 0 + -4X2 + 4X2 -35 + 3X + 4X2 = -4X2 + 4X2 Combine like terms: -4X2 + 4X2 = 0 -35 + 3X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 0.75X + X2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 0.75X + 8.75 + X2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 0.75X + X2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 0.75X + X2 = 0 + 8.75 0.75X + X2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 0.75X + X2 = 8.75 The X term is 0.75X. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75X + 0.140625 + X2 = 8.75 + 0.140625 Reorder the terms: 0.140625 + 0.75X + X2 = 8.75 + 0.140625 Combine like terms: 8.75 + 0.140625 = 8.890625 0.140625 + 0.75X + X2 = 8.890625 Factor a perfect square on the left side: (X + 0.375)(X + 0.375) = 8.890625 Calculate the square root of the right side: 2.98171511 Break this problem into two subproblems by setting (X + 0.375) equal to 2.98171511 and -2.98171511.Subproblem 1
X + 0.375 = 2.98171511 Simplifying X + 0.375 = 2.98171511 Reorder the terms: 0.375 + X = 2.98171511 Solving 0.375 + X = 2.98171511 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + X = 2.98171511 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + X = 2.98171511 + -0.375 X = 2.98171511 + -0.375 Combine like terms: 2.98171511 + -0.375 = 2.60671511 X = 2.60671511 Simplifying X = 2.60671511Subproblem 2
X + 0.375 = -2.98171511 Simplifying X + 0.375 = -2.98171511 Reorder the terms: 0.375 + X = -2.98171511 Solving 0.375 + X = -2.98171511 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + X = -2.98171511 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + X = -2.98171511 + -0.375 X = -2.98171511 + -0.375 Combine like terms: -2.98171511 + -0.375 = -3.35671511 X = -3.35671511 Simplifying X = -3.35671511Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.60671511, -3.35671511}
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