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Simplifying 12x2 + 17x + 1 = 0 Reorder the terms: 1 + 17x + 12x2 = 0 Solving 1 + 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'. 0.08333333333 + 1.416666667x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + 1.416666667x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + 1.416666667x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + 1.416666667x + x2 = 0 + -0.08333333333 1.416666667x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 1.416666667x + x2 = -0.08333333333 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 = -0.08333333333 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667x + x2 = -0.08333333333 + 0.5017361113 Combine like terms: -0.08333333333 + 0.5017361113 = 0.41840277797 0.5017361113 + 1.416666667x + x2 = 0.41840277797 Factor a perfect square on the left side: (x + 0.7083333335)(x + 0.7083333335) = 0.41840277797 Calculate the square root of the right side: 0.646840612 Break this problem into two subproblems by setting (x + 0.7083333335) equal to 0.646840612 and -0.646840612.Subproblem 1
x + 0.7083333335 = 0.646840612 Simplifying x + 0.7083333335 = 0.646840612 Reorder the terms: 0.7083333335 + x = 0.646840612 Solving 0.7083333335 + x = 0.646840612 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 = 0.646840612 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 0.646840612 + -0.7083333335 x = 0.646840612 + -0.7083333335 Combine like terms: 0.646840612 + -0.7083333335 = -0.0614927215 x = -0.0614927215 Simplifying x = -0.0614927215Subproblem 2
x + 0.7083333335 = -0.646840612 Simplifying x + 0.7083333335 = -0.646840612 Reorder the terms: 0.7083333335 + x = -0.646840612 Solving 0.7083333335 + x = -0.646840612 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 = -0.646840612 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -0.646840612 + -0.7083333335 x = -0.646840612 + -0.7083333335 Combine like terms: -0.646840612 + -0.7083333335 = -1.3551739455 x = -1.3551739455 Simplifying x = -1.3551739455Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0614927215, -1.3551739455}
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