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Simplifying 4x2 + 11x + -72 = 0 Reorder the terms: -72 + 11x + 4x2 = 0 Solving -72 + 11x + 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'. -18 + 2.75x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 2.75x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 2.75x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 2.75x + x2 = 0 + 18 2.75x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 2.75x + x2 = 18 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 18 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 18 + 1.890625 Combine like terms: 18 + 1.890625 = 19.890625 1.890625 + 2.75x + x2 = 19.890625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 19.890625 Calculate the square root of the right side: 4.459890694 Break this problem into two subproblems by setting (x + 1.375) equal to 4.459890694 and -4.459890694.Subproblem 1
x + 1.375 = 4.459890694 Simplifying x + 1.375 = 4.459890694 Reorder the terms: 1.375 + x = 4.459890694 Solving 1.375 + x = 4.459890694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 4.459890694 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 4.459890694 + -1.375 x = 4.459890694 + -1.375 Combine like terms: 4.459890694 + -1.375 = 3.084890694 x = 3.084890694 Simplifying x = 3.084890694Subproblem 2
x + 1.375 = -4.459890694 Simplifying x + 1.375 = -4.459890694 Reorder the terms: 1.375 + x = -4.459890694 Solving 1.375 + x = -4.459890694 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -4.459890694 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -4.459890694 + -1.375 x = -4.459890694 + -1.375 Combine like terms: -4.459890694 + -1.375 = -5.834890694 x = -5.834890694 Simplifying x = -5.834890694Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.084890694, -5.834890694}
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