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Simplifying 11X2 + 18X + -315 = 0 Reorder the terms: -315 + 18X + 11X2 = 0 Solving -315 + 18X + 11X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -28.63636364 + 1.636363636X + X2 = 0 Move the constant term to the right: Add '28.63636364' to each side of the equation. -28.63636364 + 1.636363636X + 28.63636364 + X2 = 0 + 28.63636364 Reorder the terms: -28.63636364 + 28.63636364 + 1.636363636X + X2 = 0 + 28.63636364 Combine like terms: -28.63636364 + 28.63636364 = 0.00000000 0.00000000 + 1.636363636X + X2 = 0 + 28.63636364 1.636363636X + X2 = 0 + 28.63636364 Combine like terms: 0 + 28.63636364 = 28.63636364 1.636363636X + X2 = 28.63636364 The X term is 1.636363636X. Take half its coefficient (0.818181818). Square it (0.6694214873) and add it to both sides. Add '0.6694214873' to each side of the equation. 1.636363636X + 0.6694214873 + X2 = 28.63636364 + 0.6694214873 Reorder the terms: 0.6694214873 + 1.636363636X + X2 = 28.63636364 + 0.6694214873 Combine like terms: 28.63636364 + 0.6694214873 = 29.3057851273 0.6694214873 + 1.636363636X + X2 = 29.3057851273 Factor a perfect square on the left side: (X + 0.818181818)(X + 0.818181818) = 29.3057851273 Calculate the square root of the right side: 5.413481793 Break this problem into two subproblems by setting (X + 0.818181818) equal to 5.413481793 and -5.413481793.Subproblem 1
X + 0.818181818 = 5.413481793 Simplifying X + 0.818181818 = 5.413481793 Reorder the terms: 0.818181818 + X = 5.413481793 Solving 0.818181818 + X = 5.413481793 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + X = 5.413481793 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + X = 5.413481793 + -0.818181818 X = 5.413481793 + -0.818181818 Combine like terms: 5.413481793 + -0.818181818 = 4.595299975 X = 4.595299975 Simplifying X = 4.595299975Subproblem 2
X + 0.818181818 = -5.413481793 Simplifying X + 0.818181818 = -5.413481793 Reorder the terms: 0.818181818 + X = -5.413481793 Solving 0.818181818 + X = -5.413481793 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + X = -5.413481793 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + X = -5.413481793 + -0.818181818 X = -5.413481793 + -0.818181818 Combine like terms: -5.413481793 + -0.818181818 = -6.231663611 X = -6.231663611 Simplifying X = -6.231663611Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.595299975, -6.231663611}
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