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Simplifying 12x2 + 17x + -12 = 0 Reorder the terms: -12 + 17x + 12x2 = 0 Solving -12 + 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'. -1 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.416666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.416666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.416666667x + x2 = 0 + 1 1.416666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.416666667x + x2 = 1 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 = 1 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = 1 + 0.5017361113 Combine like terms: 1 + 0.5017361113 = 1.5017361113 0.5017361113 + 1.416666667x + x2 = 1.5017361113 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 1.5017361113 Calculate the square root of the right side: 1.225453431 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 1.225453431 and -1.225453431.Subproblem 1
x + 0.7083333335 = 1.225453431 Simplifying x + 0.7083333335 = 1.225453431 Reorder the terms: 0.7083333335 + x = 1.225453431 Solving 0.7083333335 + x = 1.225453431 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 = 1.225453431 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 1.225453431 + -0.7083333335 x = 1.225453431 + -0.7083333335 Combine like terms: 1.225453431 + -0.7083333335 = 0.5171200975 x = 0.5171200975 Simplifying x = 0.5171200975Subproblem 2
x + 0.7083333335 = -1.225453431 Simplifying x + 0.7083333335 = -1.225453431 Reorder the terms: 0.7083333335 + x = -1.225453431 Solving 0.7083333335 + x = -1.225453431 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 = -1.225453431 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -1.225453431 + -0.7083333335 x = -1.225453431 + -0.7083333335 Combine like terms: -1.225453431 + -0.7083333335 = -1.9337867645 x = -1.9337867645 Simplifying x = -1.9337867645Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5171200975, -1.9337867645}
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