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Simplifying 6x2 + 7x = 27 Reorder the terms: 7x + 6x2 = 27 Solving 7x + 6x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 7x + 6x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.5 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 1.166666667x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 1.166666667x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 1.166666667x + x2 = 0 + 4.5 1.166666667x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 1.166666667x + x2 = 4.5 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 = 4.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 4.5 + 0.3402777780 Combine like terms: 4.5 + 0.3402777780 = 4.840277778 0.3402777780 + 1.166666667x + x2 = 4.840277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 4.840277778 Calculate the square root of the right side: 2.20006313 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 2.20006313 and -2.20006313.Subproblem 1
x + 0.5833333335 = 2.20006313 Simplifying x + 0.5833333335 = 2.20006313 Reorder the terms: 0.5833333335 + x = 2.20006313 Solving 0.5833333335 + x = 2.20006313 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 = 2.20006313 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 2.20006313 + -0.5833333335 x = 2.20006313 + -0.5833333335 Combine like terms: 2.20006313 + -0.5833333335 = 1.6167297965 x = 1.6167297965 Simplifying x = 1.6167297965Subproblem 2
x + 0.5833333335 = -2.20006313 Simplifying x + 0.5833333335 = -2.20006313 Reorder the terms: 0.5833333335 + x = -2.20006313 Solving 0.5833333335 + x = -2.20006313 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 = -2.20006313 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -2.20006313 + -0.5833333335 x = -2.20006313 + -0.5833333335 Combine like terms: -2.20006313 + -0.5833333335 = -2.7833964635 x = -2.7833964635 Simplifying x = -2.7833964635Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6167297965, -2.7833964635}
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