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Simplifying 6x2 + -7x + -53 = 0 Reorder the terms: -53 + -7x + 6x2 = 0 Solving -53 + -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'. -8.833333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '8.833333333' to each side of the equation. -8.833333333 + -1.166666667x + 8.833333333 + x2 = 0 + 8.833333333 Reorder the terms: -8.833333333 + 8.833333333 + -1.166666667x + x2 = 0 + 8.833333333 Combine like terms: -8.833333333 + 8.833333333 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 8.833333333 -1.166666667x + x2 = 0 + 8.833333333 Combine like terms: 0 + 8.833333333 = 8.833333333 -1.166666667x + x2 = 8.833333333 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 = 8.833333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 8.833333333 + 0.3402777780 Combine like terms: 8.833333333 + 0.3402777780 = 9.173611111 0.3402777780 + -1.166666667x + x2 = 9.173611111 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 9.173611111 Calculate the square root of the right side: 3.028796974 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 3.028796974 and -3.028796974.Subproblem 1
x + -0.5833333335 = 3.028796974 Simplifying x + -0.5833333335 = 3.028796974 Reorder the terms: -0.5833333335 + x = 3.028796974 Solving -0.5833333335 + x = 3.028796974 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 = 3.028796974 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 3.028796974 + 0.5833333335 x = 3.028796974 + 0.5833333335 Combine like terms: 3.028796974 + 0.5833333335 = 3.6121303075 x = 3.6121303075 Simplifying x = 3.6121303075Subproblem 2
x + -0.5833333335 = -3.028796974 Simplifying x + -0.5833333335 = -3.028796974 Reorder the terms: -0.5833333335 + x = -3.028796974 Solving -0.5833333335 + x = -3.028796974 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 = -3.028796974 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -3.028796974 + 0.5833333335 x = -3.028796974 + 0.5833333335 Combine like terms: -3.028796974 + 0.5833333335 = -2.4454636405 x = -2.4454636405 Simplifying x = -2.4454636405Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6121303075, -2.4454636405}
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