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Simplifying 6x2 + -7x + -196 = 0 Reorder the terms: -196 + -7x + 6x2 = 0 Solving -196 + -7x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -32.66666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '32.66666667' to each side of the equation. -32.66666667 + -1.166666667x + 32.66666667 + x2 = 0 + 32.66666667 Reorder the terms: -32.66666667 + 32.66666667 + -1.166666667x + x2 = 0 + 32.66666667 Combine like terms: -32.66666667 + 32.66666667 = 0.00000000 0.00000000 + -1.166666667x + x2 = 0 + 32.66666667 -1.166666667x + x2 = 0 + 32.66666667 Combine like terms: 0 + 32.66666667 = 32.66666667 -1.166666667x + x2 = 32.66666667 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 32.66666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 32.66666667 + 0.3402777780 Combine like terms: 32.66666667 + 0.3402777780 = 33.006944448 0.3402777780 + -1.166666667x + x2 = 33.006944448 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 33.006944448 Calculate the square root of the right side: 5.745167051 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 5.745167051 and -5.745167051.Subproblem 1
x + -0.5833333335 = 5.745167051 Simplifying x + -0.5833333335 = 5.745167051 Reorder the terms: -0.5833333335 + x = 5.745167051 Solving -0.5833333335 + x = 5.745167051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 5.745167051 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 5.745167051 + 0.5833333335 x = 5.745167051 + 0.5833333335 Combine like terms: 5.745167051 + 0.5833333335 = 6.3285003845 x = 6.3285003845 Simplifying x = 6.3285003845Subproblem 2
x + -0.5833333335 = -5.745167051 Simplifying x + -0.5833333335 = -5.745167051 Reorder the terms: -0.5833333335 + x = -5.745167051 Solving -0.5833333335 + x = -5.745167051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -5.745167051 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -5.745167051 + 0.5833333335 x = -5.745167051 + 0.5833333335 Combine like terms: -5.745167051 + 0.5833333335 = -5.1618337175 x = -5.1618337175 Simplifying x = -5.1618337175Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.3285003845, -5.1618337175}
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