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Simplifying 4x2 + 11x + -8 = 0 Reorder the terms: -8 + 11x + 4x2 = 0 Solving -8 + 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'. -2 + 2.75x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.75x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.75x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.75x + x2 = 0 + 2 2.75x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.75x + x2 = 2 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 = 2 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 2 + 1.890625 Combine like terms: 2 + 1.890625 = 3.890625 1.890625 + 2.75x + x2 = 3.890625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + 1.375) equal to 1.97246673 and -1.97246673.Subproblem 1
x + 1.375 = 1.97246673 Simplifying x + 1.375 = 1.97246673 Reorder the terms: 1.375 + x = 1.97246673 Solving 1.375 + x = 1.97246673 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 = 1.97246673 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.97246673 + -1.375 x = 1.97246673 + -1.375 Combine like terms: 1.97246673 + -1.375 = 0.59746673 x = 0.59746673 Simplifying x = 0.59746673Subproblem 2
x + 1.375 = -1.97246673 Simplifying x + 1.375 = -1.97246673 Reorder the terms: 1.375 + x = -1.97246673 Solving 1.375 + x = -1.97246673 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 = -1.97246673 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.97246673 + -1.375 x = -1.97246673 + -1.375 Combine like terms: -1.97246673 + -1.375 = -3.34746673 x = -3.34746673 Simplifying x = -3.34746673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.59746673, -3.34746673}
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