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Simplifying 384 + -400x = -56x2 + -1x Reorder the terms: 384 + -400x = -1x + -56x2 Solving 384 + -400x = -1x + -56x2 Solving for variable 'x'. Combine like terms: -400x + x = -399x 384 + -399x + 56x2 = -1x + -56x2 + x + 56x2 Reorder the terms: 384 + -399x + 56x2 = -1x + x + -56x2 + 56x2 Combine like terms: -1x + x = 0 384 + -399x + 56x2 = 0 + -56x2 + 56x2 384 + -399x + 56x2 = -56x2 + 56x2 Combine like terms: -56x2 + 56x2 = 0 384 + -399x + 56x2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. 6.857142857 + -7.125x + x2 = 0 Move the constant term to the right: Add '-6.857142857' to each side of the equation. 6.857142857 + -7.125x + -6.857142857 + x2 = 0 + -6.857142857 Reorder the terms: 6.857142857 + -6.857142857 + -7.125x + x2 = 0 + -6.857142857 Combine like terms: 6.857142857 + -6.857142857 = 0.000000000 0.000000000 + -7.125x + x2 = 0 + -6.857142857 -7.125x + x2 = 0 + -6.857142857 Combine like terms: 0 + -6.857142857 = -6.857142857 -7.125x + x2 = -6.857142857 The x term is -7.125x. Take half its coefficient (-3.5625). Square it (12.69140625) and add it to both sides. Add '12.69140625' to each side of the equation. -7.125x + 12.69140625 + x2 = -6.857142857 + 12.69140625 Reorder the terms: 12.69140625 + -7.125x + x2 = -6.857142857 + 12.69140625 Combine like terms: -6.857142857 + 12.69140625 = 5.834263393 12.69140625 + -7.125x + x2 = 5.834263393 Factor a perfect square on the left side: (x + -3.5625)(x + -3.5625) = 5.834263393 Calculate the square root of the right side: 2.415421991 Break this problem into two subproblems by setting (x + -3.5625) equal to 2.415421991 and -2.415421991.Subproblem 1
x + -3.5625 = 2.415421991 Simplifying x + -3.5625 = 2.415421991 Reorder the terms: -3.5625 + x = 2.415421991 Solving -3.5625 + x = 2.415421991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + x = 2.415421991 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + x = 2.415421991 + 3.5625 x = 2.415421991 + 3.5625 Combine like terms: 2.415421991 + 3.5625 = 5.977921991 x = 5.977921991 Simplifying x = 5.977921991Subproblem 2
x + -3.5625 = -2.415421991 Simplifying x + -3.5625 = -2.415421991 Reorder the terms: -3.5625 + x = -2.415421991 Solving -3.5625 + x = -2.415421991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + x = -2.415421991 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + x = -2.415421991 + 3.5625 x = -2.415421991 + 3.5625 Combine like terms: -2.415421991 + 3.5625 = 1.147078009 x = 1.147078009 Simplifying x = 1.147078009Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.977921991, 1.147078009}
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