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Simplifying 4x2 + 27x + 30 = 0 Reorder the terms: 30 + 27x + 4x2 = 0 Solving 30 + 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'. 7.5 + 6.75x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 6.75x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 6.75x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 6.75x + x2 = 0 + -7.5 6.75x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 6.75x + x2 = -7.5 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 = -7.5 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -7.5 + 11.390625 Combine like terms: -7.5 + 11.390625 = 3.890625 11.390625 + 6.75x + x2 = 3.890625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + 3.375) equal to 1.97246673 and -1.97246673.Subproblem 1
x + 3.375 = 1.97246673 Simplifying x + 3.375 = 1.97246673 Reorder the terms: 3.375 + x = 1.97246673 Solving 3.375 + x = 1.97246673 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 = 1.97246673 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 1.97246673 + -3.375 x = 1.97246673 + -3.375 Combine like terms: 1.97246673 + -3.375 = -1.40253327 x = -1.40253327 Simplifying x = -1.40253327Subproblem 2
x + 3.375 = -1.97246673 Simplifying x + 3.375 = -1.97246673 Reorder the terms: 3.375 + x = -1.97246673 Solving 3.375 + x = -1.97246673 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 = -1.97246673 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -1.97246673 + -3.375 x = -1.97246673 + -3.375 Combine like terms: -1.97246673 + -3.375 = -5.34746673 x = -5.34746673 Simplifying x = -5.34746673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.40253327, -5.34746673}
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