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Simplifying 17x + -94 + 12x2 = 0 Reorder the terms: -94 + 17x + 12x2 = 0 Solving -94 + 17x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -7.833333333 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '7.833333333' to each side of the equation. -7.833333333 + 1.416666667x + 7.833333333 + x2 = 0 + 7.833333333 Reorder the terms: -7.833333333 + 7.833333333 + 1.416666667x + x2 = 0 + 7.833333333 Combine like terms: -7.833333333 + 7.833333333 = 0.000000000 0.000000000 + 1.416666667x + x2 = 0 + 7.833333333 1.416666667x + x2 = 0 + 7.833333333 Combine like terms: 0 + 7.833333333 = 7.833333333 1.416666667x + x2 = 7.833333333 The x term is 1.416666667x. Take half its coefficient (0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. 1.416666667x + 0.5017361113 + x2 = 7.833333333 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = 7.833333333 + 0.5017361113 Combine like terms: 7.833333333 + 0.5017361113 = 8.3350694443 0.5017361113 + 1.416666667x + x2 = 8.3350694443 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 8.3350694443 Calculate the square root of the right side: 2.887052034 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 2.887052034 and -2.887052034.Subproblem 1
x + 0.7083333335 = 2.887052034 Simplifying x + 0.7083333335 = 2.887052034 Reorder the terms: 0.7083333335 + x = 2.887052034 Solving 0.7083333335 + x = 2.887052034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = 2.887052034 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 2.887052034 + -0.7083333335 x = 2.887052034 + -0.7083333335 Combine like terms: 2.887052034 + -0.7083333335 = 2.1787187005 x = 2.1787187005 Simplifying x = 2.1787187005Subproblem 2
x + 0.7083333335 = -2.887052034 Simplifying x + 0.7083333335 = -2.887052034 Reorder the terms: 0.7083333335 + x = -2.887052034 Solving 0.7083333335 + x = -2.887052034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = -2.887052034 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -2.887052034 + -0.7083333335 x = -2.887052034 + -0.7083333335 Combine like terms: -2.887052034 + -0.7083333335 = -3.5953853675 x = -3.5953853675 Simplifying x = -3.5953853675Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1787187005, -3.5953853675}
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