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Simplifying 4x2 + -11x + -80 = 0 Reorder the terms: -80 + -11x + 4x2 = 0 Solving -80 + -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'. -20 + -2.75x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -2.75x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -2.75x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2.75x + x2 = 0 + 20 -2.75x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2.75x + x2 = 20 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 = 20 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 20 + 1.890625 Combine like terms: 20 + 1.890625 = 21.890625 1.890625 + -2.75x + x2 = 21.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 21.890625 Calculate the square root of the right side: 4.678741818 Break this problem into two subproblems by setting (x + -1.375) equal to 4.678741818 and -4.678741818.Subproblem 1
x + -1.375 = 4.678741818 Simplifying x + -1.375 = 4.678741818 Reorder the terms: -1.375 + x = 4.678741818 Solving -1.375 + x = 4.678741818 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 = 4.678741818 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 4.678741818 + 1.375 x = 4.678741818 + 1.375 Combine like terms: 4.678741818 + 1.375 = 6.053741818 x = 6.053741818 Simplifying x = 6.053741818Subproblem 2
x + -1.375 = -4.678741818 Simplifying x + -1.375 = -4.678741818 Reorder the terms: -1.375 + x = -4.678741818 Solving -1.375 + x = -4.678741818 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 = -4.678741818 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -4.678741818 + 1.375 x = -4.678741818 + 1.375 Combine like terms: -4.678741818 + 1.375 = -3.303741818 x = -3.303741818 Simplifying x = -3.303741818Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.053741818, -3.303741818}
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