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Simplifying 18x2 + -21x + -49 = 180 Reorder the terms: -49 + -21x + 18x2 = 180 Solving -49 + -21x + 18x2 = 180 Solving for variable 'x'. Reorder the terms: -49 + -180 + -21x + 18x2 = 180 + -180 Combine like terms: -49 + -180 = -229 -229 + -21x + 18x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -229 + -21x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -12.72222222 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '12.72222222' to each side of the equation. -12.72222222 + -1.166666667x + 12.72222222 + x2 = 0 + 12.72222222 Reorder the terms: -12.72222222 + 12.72222222 + -1.166666667x + x2 = 0 + 12.72222222 Combine like terms: -12.72222222 + 12.72222222 = 0.00000000 0.00000000 + -1.166666667x + x2 = 0 + 12.72222222 -1.166666667x + x2 = 0 + 12.72222222 Combine like terms: 0 + 12.72222222 = 12.72222222 -1.166666667x + x2 = 12.72222222 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 = 12.72222222 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 12.72222222 + 0.3402777780 Combine like terms: 12.72222222 + 0.3402777780 = 13.062499998 0.3402777780 + -1.166666667x + x2 = 13.062499998 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 13.062499998 Calculate the square root of the right side: 3.614208073 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 3.614208073 and -3.614208073.Subproblem 1
x + -0.5833333335 = 3.614208073 Simplifying x + -0.5833333335 = 3.614208073 Reorder the terms: -0.5833333335 + x = 3.614208073 Solving -0.5833333335 + x = 3.614208073 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 = 3.614208073 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 3.614208073 + 0.5833333335 x = 3.614208073 + 0.5833333335 Combine like terms: 3.614208073 + 0.5833333335 = 4.1975414065 x = 4.1975414065 Simplifying x = 4.1975414065Subproblem 2
x + -0.5833333335 = -3.614208073 Simplifying x + -0.5833333335 = -3.614208073 Reorder the terms: -0.5833333335 + x = -3.614208073 Solving -0.5833333335 + x = -3.614208073 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 = -3.614208073 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -3.614208073 + 0.5833333335 x = -3.614208073 + 0.5833333335 Combine like terms: -3.614208073 + 0.5833333335 = -3.0308747395 x = -3.0308747395 Simplifying x = -3.0308747395Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1975414065, -3.0308747395}
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