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Simplifying 4x2 + -11x + -40 = 0 Reorder the terms: -40 + -11x + 4x2 = 0 Solving -40 + -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'. -10 + -2.75x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -2.75x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -2.75x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2.75x + x2 = 0 + 10 -2.75x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2.75x + x2 = 10 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 = 10 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 10 + 1.890625 Combine like terms: 10 + 1.890625 = 11.890625 1.890625 + -2.75x + x2 = 11.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 11.890625 Calculate the square root of the right side: 3.448278556 Break this problem into two subproblems by setting (x + -1.375) equal to 3.448278556 and -3.448278556.Subproblem 1
x + -1.375 = 3.448278556 Simplifying x + -1.375 = 3.448278556 Reorder the terms: -1.375 + x = 3.448278556 Solving -1.375 + x = 3.448278556 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 = 3.448278556 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 3.448278556 + 1.375 x = 3.448278556 + 1.375 Combine like terms: 3.448278556 + 1.375 = 4.823278556 x = 4.823278556 Simplifying x = 4.823278556Subproblem 2
x + -1.375 = -3.448278556 Simplifying x + -1.375 = -3.448278556 Reorder the terms: -1.375 + x = -3.448278556 Solving -1.375 + x = -3.448278556 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 = -3.448278556 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -3.448278556 + 1.375 x = -3.448278556 + 1.375 Combine like terms: -3.448278556 + 1.375 = -2.073278556 x = -2.073278556 Simplifying x = -2.073278556Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.823278556, -2.073278556}
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