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Simplifying 4x2 + -11x + -103 = 0 Reorder the terms: -103 + -11x + 4x2 = 0 Solving -103 + -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'. -25.75 + -2.75x + x2 = 0 Move the constant term to the right: Add '25.75' to each side of the equation. -25.75 + -2.75x + 25.75 + x2 = 0 + 25.75 Reorder the terms: -25.75 + 25.75 + -2.75x + x2 = 0 + 25.75 Combine like terms: -25.75 + 25.75 = 0.00 0.00 + -2.75x + x2 = 0 + 25.75 -2.75x + x2 = 0 + 25.75 Combine like terms: 0 + 25.75 = 25.75 -2.75x + x2 = 25.75 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 = 25.75 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 25.75 + 1.890625 Combine like terms: 25.75 + 1.890625 = 27.640625 1.890625 + -2.75x + x2 = 27.640625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 27.640625 Calculate the square root of the right side: 5.257435211 Break this problem into two subproblems by setting (x + -1.375) equal to 5.257435211 and -5.257435211.Subproblem 1
x + -1.375 = 5.257435211 Simplifying x + -1.375 = 5.257435211 Reorder the terms: -1.375 + x = 5.257435211 Solving -1.375 + x = 5.257435211 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 = 5.257435211 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 5.257435211 + 1.375 x = 5.257435211 + 1.375 Combine like terms: 5.257435211 + 1.375 = 6.632435211 x = 6.632435211 Simplifying x = 6.632435211Subproblem 2
x + -1.375 = -5.257435211 Simplifying x + -1.375 = -5.257435211 Reorder the terms: -1.375 + x = -5.257435211 Solving -1.375 + x = -5.257435211 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 = -5.257435211 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -5.257435211 + 1.375 x = -5.257435211 + 1.375 Combine like terms: -5.257435211 + 1.375 = -3.882435211 x = -3.882435211 Simplifying x = -3.882435211Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.632435211, -3.882435211}
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