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Simplifying 5.6 = 5.6x2 + 5.6x + x Reorder the terms: 5.6 = 5.6x + x + 5.6x2 Combine like terms: 5.6x + x = 6.6x 5.6 = 6.6x + 5.6x2 Solving 5.6 = 6.6x + 5.6x2 Solving for variable 'x'. Reorder the terms: 5.6 + -6.6x + -5.6x2 = 6.6x + -6.6x + 5.6x2 + -5.6x2 Combine like terms: 6.6x + -6.6x = 0.0 5.6 + -6.6x + -5.6x2 = 0.0 + 5.6x2 + -5.6x2 5.6 + -6.6x + -5.6x2 = 5.6x2 + -5.6x2 Combine like terms: 5.6x2 + -5.6x2 = 0.0 5.6 + -6.6x + -5.6x2 = 0.0 Begin completing the square. Divide all terms by -5.6 the coefficient of the squared term: Divide each side by '-5.6'. -1 + 1.178571429x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.178571429x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.178571429x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.178571429x + x2 = 0 + 1 1.178571429x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.178571429x + x2 = 1 The x term is 1.178571429x. Take half its coefficient (0.5892857145). Square it (0.3472576533) and add it to both sides. Add '0.3472576533' to each side of the equation. 1.178571429x + 0.3472576533 + x2 = 1 + 0.3472576533 Reorder the terms: 0.3472576533 + 1.178571429x + x2 = 1 + 0.3472576533 Combine like terms: 1 + 0.3472576533 = 1.3472576533 0.3472576533 + 1.178571429x + x2 = 1.3472576533 Factor a perfect square on the left side: (x + 0.5892857145)(x + 0.5892857145) = 1.3472576533 Calculate the square root of the right side: 1.160714286 Break this problem into two subproblems by setting (x + 0.5892857145) equal to 1.160714286 and -1.160714286.Subproblem 1
x + 0.5892857145 = 1.160714286 Simplifying x + 0.5892857145 = 1.160714286 Reorder the terms: 0.5892857145 + x = 1.160714286 Solving 0.5892857145 + x = 1.160714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5892857145' to each side of the equation. 0.5892857145 + -0.5892857145 + x = 1.160714286 + -0.5892857145 Combine like terms: 0.5892857145 + -0.5892857145 = 0.0000000000 0.0000000000 + x = 1.160714286 + -0.5892857145 x = 1.160714286 + -0.5892857145 Combine like terms: 1.160714286 + -0.5892857145 = 0.5714285715 x = 0.5714285715 Simplifying x = 0.5714285715Subproblem 2
x + 0.5892857145 = -1.160714286 Simplifying x + 0.5892857145 = -1.160714286 Reorder the terms: 0.5892857145 + x = -1.160714286 Solving 0.5892857145 + x = -1.160714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5892857145' to each side of the equation. 0.5892857145 + -0.5892857145 + x = -1.160714286 + -0.5892857145 Combine like terms: 0.5892857145 + -0.5892857145 = 0.0000000000 0.0000000000 + x = -1.160714286 + -0.5892857145 x = -1.160714286 + -0.5892857145 Combine like terms: -1.160714286 + -0.5892857145 = -1.7500000005 x = -1.7500000005 Simplifying x = -1.7500000005Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5714285715, -1.7500000005}
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