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Simplifying -18x2 + -21x + 22 = -396 Reorder the terms: 22 + -21x + -18x2 = -396 Solving 22 + -21x + -18x2 = -396 Solving for variable 'x'. Reorder the terms: 22 + 396 + -21x + -18x2 = -396 + 396 Combine like terms: 22 + 396 = 418 418 + -21x + -18x2 = -396 + 396 Combine like terms: -396 + 396 = 0 418 + -21x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -23.22222222 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '23.22222222' to each side of the equation. -23.22222222 + 1.166666667x + 23.22222222 + x2 = 0 + 23.22222222 Reorder the terms: -23.22222222 + 23.22222222 + 1.166666667x + x2 = 0 + 23.22222222 Combine like terms: -23.22222222 + 23.22222222 = 0.00000000 0.00000000 + 1.166666667x + x2 = 0 + 23.22222222 1.166666667x + x2 = 0 + 23.22222222 Combine like terms: 0 + 23.22222222 = 23.22222222 1.166666667x + x2 = 23.22222222 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 = 23.22222222 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 23.22222222 + 0.3402777780 Combine like terms: 23.22222222 + 0.3402777780 = 23.562499998 0.3402777780 + 1.166666667x + x2 = 23.562499998 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 23.562499998 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 4.85412196 and -4.85412196.Subproblem 1
x + 0.5833333335 = 4.85412196 Simplifying x + 0.5833333335 = 4.85412196 Reorder the terms: 0.5833333335 + x = 4.85412196 Solving 0.5833333335 + x = 4.85412196 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 = 4.85412196 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 4.85412196 + -0.5833333335 x = 4.85412196 + -0.5833333335 Combine like terms: 4.85412196 + -0.5833333335 = 4.2707886265 x = 4.2707886265 Simplifying x = 4.2707886265Subproblem 2
x + 0.5833333335 = -4.85412196 Simplifying x + 0.5833333335 = -4.85412196 Reorder the terms: 0.5833333335 + x = -4.85412196 Solving 0.5833333335 + x = -4.85412196 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 = -4.85412196 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -4.85412196 + -0.5833333335 x = -4.85412196 + -0.5833333335 Combine like terms: -4.85412196 + -0.5833333335 = -5.4374552935 x = -5.4374552935 Simplifying x = -5.4374552935Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2707886265, -5.4374552935}
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