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Simplifying x2 + 103680x + -103680 = 0 Reorder the terms: -103680 + 103680x + x2 = 0 Solving -103680 + 103680x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '103680' to each side of the equation. -103680 + 103680x + 103680 + x2 = 0 + 103680 Reorder the terms: -103680 + 103680 + 103680x + x2 = 0 + 103680 Combine like terms: -103680 + 103680 = 0 0 + 103680x + x2 = 0 + 103680 103680x + x2 = 0 + 103680 Combine like terms: 0 + 103680 = 103680 103680x + x2 = 103680 The x term is 103680x. Take half its coefficient (51840). Square it (2687385600) and add it to both sides. Add '2687385600' to each side of the equation. 103680x + 2687385600 + x2 = 103680 + 2687385600 Reorder the terms: 2687385600 + 103680x + x2 = 103680 + 2687385600 Combine like terms: 103680 + 2687385600 = 2687489280 2687385600 + 103680x + x2 = 2687489280 Factor a perfect square on the left side: (x + 51840)(x + 51840) = 2687489280 Calculate the square root of the right side: 51840.999990355 Break this problem into two subproblems by setting (x + 51840) equal to 51840.999990355 and -51840.999990355.Subproblem 1
x + 51840 = 51840.999990355 Simplifying x + 51840 = 51840.999990355 Reorder the terms: 51840 + x = 51840.999990355 Solving 51840 + x = 51840.999990355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51840' to each side of the equation. 51840 + -51840 + x = 51840.999990355 + -51840 Combine like terms: 51840 + -51840 = 0 0 + x = 51840.999990355 + -51840 x = 51840.999990355 + -51840 Combine like terms: 51840.999990355 + -51840 = 0.999990355 x = 0.999990355 Simplifying x = 0.999990355Subproblem 2
x + 51840 = -51840.999990355 Simplifying x + 51840 = -51840.999990355 Reorder the terms: 51840 + x = -51840.999990355 Solving 51840 + x = -51840.999990355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51840' to each side of the equation. 51840 + -51840 + x = -51840.999990355 + -51840 Combine like terms: 51840 + -51840 = 0 0 + x = -51840.999990355 + -51840 x = -51840.999990355 + -51840 Combine like terms: -51840.999990355 + -51840 = -103680.999990355 x = -103680.999990355 Simplifying x = -103680.999990355Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.999990355, -103680.999990355}
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