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Simplifying -4x2 + 11x + 5 = 0 Reorder the terms: 5 + 11x + -4x2 = 0 Solving 5 + 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'. -1.25 + -2.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.75x + x2 = 0 + 1.25 -2.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.75x + x2 = 1.25 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 = 1.25 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 1.25 + 1.890625 Combine like terms: 1.25 + 1.890625 = 3.140625 1.890625 + -2.75x + x2 = 3.140625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + -1.375) equal to 1.77218086 and -1.77218086.Subproblem 1
x + -1.375 = 1.77218086 Simplifying x + -1.375 = 1.77218086 Reorder the terms: -1.375 + x = 1.77218086 Solving -1.375 + x = 1.77218086 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 = 1.77218086 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.77218086 + 1.375 x = 1.77218086 + 1.375 Combine like terms: 1.77218086 + 1.375 = 3.14718086 x = 3.14718086 Simplifying x = 3.14718086Subproblem 2
x + -1.375 = -1.77218086 Simplifying x + -1.375 = -1.77218086 Reorder the terms: -1.375 + x = -1.77218086 Solving -1.375 + x = -1.77218086 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 = -1.77218086 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.77218086 + 1.375 x = -1.77218086 + 1.375 Combine like terms: -1.77218086 + 1.375 = -0.39718086 x = -0.39718086 Simplifying x = -0.39718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.14718086, -0.39718086}
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