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Simplifying x(4x + -11) + -11 = 20 Reorder the terms: x(-11 + 4x) + -11 = 20 (-11 * x + 4x * x) + -11 = 20 (-11x + 4x2) + -11 = 20 Reorder the terms: -11 + -11x + 4x2 = 20 Solving -11 + -11x + 4x2 = 20 Solving for variable 'x'. Reorder the terms: -11 + -20 + -11x + 4x2 = 20 + -20 Combine like terms: -11 + -20 = -31 -31 + -11x + 4x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -31 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.75 + -2.75x + x2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + -2.75x + 7.75 + x2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + -2.75x + x2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + -2.75x + x2 = 0 + 7.75 -2.75x + x2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 -2.75x + x2 = 7.75 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 = 7.75 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 7.75 + 1.890625 Combine like terms: 7.75 + 1.890625 = 9.640625 1.890625 + -2.75x + x2 = 9.640625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 9.640625 Calculate the square root of the right side: 3.104935587 Break this problem into two subproblems by setting (x + -1.375) equal to 3.104935587 and -3.104935587.Subproblem 1
x + -1.375 = 3.104935587 Simplifying x + -1.375 = 3.104935587 Reorder the terms: -1.375 + x = 3.104935587 Solving -1.375 + x = 3.104935587 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 = 3.104935587 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 3.104935587 + 1.375 x = 3.104935587 + 1.375 Combine like terms: 3.104935587 + 1.375 = 4.479935587 x = 4.479935587 Simplifying x = 4.479935587Subproblem 2
x + -1.375 = -3.104935587 Simplifying x + -1.375 = -3.104935587 Reorder the terms: -1.375 + x = -3.104935587 Solving -1.375 + x = -3.104935587 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 = -3.104935587 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -3.104935587 + 1.375 x = -3.104935587 + 1.375 Combine like terms: -3.104935587 + 1.375 = -1.729935587 x = -1.729935587 Simplifying x = -1.729935587Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.479935587, -1.729935587}
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