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Simplifying 6x2 + 7x + 3 = 26 Reorder the terms: 3 + 7x + 6x2 = 26 Solving 3 + 7x + 6x2 = 26 Solving for variable 'x'. Reorder the terms: 3 + -26 + 7x + 6x2 = 26 + -26 Combine like terms: 3 + -26 = -23 -23 + 7x + 6x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -23 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.833333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '3.833333333' to each side of the equation. -3.833333333 + 1.166666667x + 3.833333333 + x2 = 0 + 3.833333333 Reorder the terms: -3.833333333 + 3.833333333 + 1.166666667x + x2 = 0 + 3.833333333 Combine like terms: -3.833333333 + 3.833333333 = 0.000000000 0.000000000 + 1.166666667x + x2 = 0 + 3.833333333 1.166666667x + x2 = 0 + 3.833333333 Combine like terms: 0 + 3.833333333 = 3.833333333 1.166666667x + x2 = 3.833333333 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 = 3.833333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 3.833333333 + 0.3402777780 Combine like terms: 3.833333333 + 0.3402777780 = 4.173611111 0.3402777780 + 1.166666667x + x2 = 4.173611111 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 4.173611111 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 2.042941779 and -2.042941779.Subproblem 1
x + 0.5833333335 = 2.042941779 Simplifying x + 0.5833333335 = 2.042941779 Reorder the terms: 0.5833333335 + x = 2.042941779 Solving 0.5833333335 + x = 2.042941779 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 = 2.042941779 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 2.042941779 + -0.5833333335 x = 2.042941779 + -0.5833333335 Combine like terms: 2.042941779 + -0.5833333335 = 1.4596084455 x = 1.4596084455 Simplifying x = 1.4596084455Subproblem 2
x + 0.5833333335 = -2.042941779 Simplifying x + 0.5833333335 = -2.042941779 Reorder the terms: 0.5833333335 + x = -2.042941779 Solving 0.5833333335 + x = -2.042941779 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 = -2.042941779 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -2.042941779 + -0.5833333335 x = -2.042941779 + -0.5833333335 Combine like terms: -2.042941779 + -0.5833333335 = -2.6262751125 x = -2.6262751125 Simplifying x = -2.6262751125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4596084455, -2.6262751125}
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