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Simplifying 12x2 + 17x + 3 = 0 Reorder the terms: 3 + 17x + 12x2 = 0 Solving 3 + 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'. 0.25 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.416666667x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.416666667x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.416666667x + x2 = 0 + -0.25 1.416666667x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.416666667x + x2 = -0.25 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 = -0.25 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = -0.25 + 0.5017361113 Combine like terms: -0.25 + 0.5017361113 = 0.2517361113 0.5017361113 + 1.416666667x + x2 = 0.2517361113 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 0.2517361113 Calculate the square root of the right side: 0.501733108 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 0.501733108 and -0.501733108.Subproblem 1
x + 0.7083333335 = 0.501733108 Simplifying x + 0.7083333335 = 0.501733108 Reorder the terms: 0.7083333335 + x = 0.501733108 Solving 0.7083333335 + x = 0.501733108 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 = 0.501733108 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 0.501733108 + -0.7083333335 x = 0.501733108 + -0.7083333335 Combine like terms: 0.501733108 + -0.7083333335 = -0.2066002255 x = -0.2066002255 Simplifying x = -0.2066002255Subproblem 2
x + 0.7083333335 = -0.501733108 Simplifying x + 0.7083333335 = -0.501733108 Reorder the terms: 0.7083333335 + x = -0.501733108 Solving 0.7083333335 + x = -0.501733108 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 = -0.501733108 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -0.501733108 + -0.7083333335 x = -0.501733108 + -0.7083333335 Combine like terms: -0.501733108 + -0.7083333335 = -1.2100664415 x = -1.2100664415 Simplifying x = -1.2100664415Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2066002255, -1.2100664415}
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