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Simplifying 123 + -1x2 = 5x + 1 Reorder the terms: 123 + -1x2 = 1 + 5x Solving 123 + -1x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: 123 + -1 + -5x + -1x2 = 1 + 5x + -1 + -5x Combine like terms: 123 + -1 = 122 122 + -5x + -1x2 = 1 + 5x + -1 + -5x Reorder the terms: 122 + -5x + -1x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 122 + -5x + -1x2 = 0 + 5x + -5x 122 + -5x + -1x2 = 5x + -5x Combine like terms: 5x + -5x = 0 122 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -122 + 5x + x2 = 0 Move the constant term to the right: Add '122' to each side of the equation. -122 + 5x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + 5x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + 5x + x2 = 0 + 122 5x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 5x + x2 = 122 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 122 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 122 + 6.25 Combine like terms: 122 + 6.25 = 128.25 6.25 + 5x + x2 = 128.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + 2.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + 2.5 = 11.324751653 Simplifying x + 2.5 = 11.324751653 Reorder the terms: 2.5 + x = 11.324751653 Solving 2.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 11.324751653 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.324751653 + -2.5 x = 11.324751653 + -2.5 Combine like terms: 11.324751653 + -2.5 = 8.824751653 x = 8.824751653 Simplifying x = 8.824751653Subproblem 2
x + 2.5 = -11.324751653 Simplifying x + 2.5 = -11.324751653 Reorder the terms: 2.5 + x = -11.324751653 Solving 2.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -11.324751653 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.324751653 + -2.5 x = -11.324751653 + -2.5 Combine like terms: -11.324751653 + -2.5 = -13.824751653 x = -13.824751653 Simplifying x = -13.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.824751653, -13.824751653}
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