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Simplifying 6x(x + -1) = x + 7 Reorder the terms: 6x(-1 + x) = x + 7 (-1 * 6x + x * 6x) = x + 7 (-6x + 6x2) = x + 7 Reorder the terms: -6x + 6x2 = 7 + x Solving -6x + 6x2 = 7 + x Solving for variable 'x'. Reorder the terms: -7 + -6x + -1x + 6x2 = 7 + x + -7 + -1x Combine like terms: -6x + -1x = -7x -7 + -7x + 6x2 = 7 + x + -7 + -1x Reorder the terms: -7 + -7x + 6x2 = 7 + -7 + x + -1x Combine like terms: 7 + -7 = 0 -7 + -7x + 6x2 = 0 + x + -1x -7 + -7x + 6x2 = x + -1x Combine like terms: x + -1x = 0 -7 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -1.166666667x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -1.166666667x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 1.166666667 -1.166666667x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -1.166666667x + x2 = 1.166666667 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 = 1.166666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 1.166666667 + 0.3402777780 Combine like terms: 1.166666667 + 0.3402777780 = 1.506944445 0.3402777780 + -1.166666667x + x2 = 1.506944445 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 1.506944445 Calculate the square root of the right side: 1.227576655 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.227576655 and -1.227576655.Subproblem 1
x + -0.5833333335 = 1.227576655 Simplifying x + -0.5833333335 = 1.227576655 Reorder the terms: -0.5833333335 + x = 1.227576655 Solving -0.5833333335 + x = 1.227576655 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 = 1.227576655 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.227576655 + 0.5833333335 x = 1.227576655 + 0.5833333335 Combine like terms: 1.227576655 + 0.5833333335 = 1.8109099885 x = 1.8109099885 Simplifying x = 1.8109099885Subproblem 2
x + -0.5833333335 = -1.227576655 Simplifying x + -0.5833333335 = -1.227576655 Reorder the terms: -0.5833333335 + x = -1.227576655 Solving -0.5833333335 + x = -1.227576655 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 = -1.227576655 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.227576655 + 0.5833333335 x = -1.227576655 + 0.5833333335 Combine like terms: -1.227576655 + 0.5833333335 = -0.6442433215 x = -0.6442433215 Simplifying x = -0.6442433215Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8109099885, -0.6442433215}
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