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Simplifying x2 + 17x = 56 Reorder the terms: 17x + x2 = 56 Solving 17x + x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 17x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 17x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 17x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 17x + x2 = 0 + 56 17x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 17x + x2 = 56 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 56 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 56 + 72.25 Combine like terms: 56 + 72.25 = 128.25 72.25 + 17x + x2 = 128.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + 8.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + 8.5 = 11.324751653 Simplifying x + 8.5 = 11.324751653 Reorder the terms: 8.5 + x = 11.324751653 Solving 8.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 11.324751653 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 11.324751653 + -8.5 x = 11.324751653 + -8.5 Combine like terms: 11.324751653 + -8.5 = 2.824751653 x = 2.824751653 Simplifying x = 2.824751653Subproblem 2
x + 8.5 = -11.324751653 Simplifying x + 8.5 = -11.324751653 Reorder the terms: 8.5 + x = -11.324751653 Solving 8.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -11.324751653 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -11.324751653 + -8.5 x = -11.324751653 + -8.5 Combine like terms: -11.324751653 + -8.5 = -19.824751653 x = -19.824751653 Simplifying x = -19.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.824751653, -19.824751653}
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