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Simplifying 18x2 + 21x + 2 = 0 Reorder the terms: 2 + 21x + 18x2 = 0 Solving 2 + 21x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.1111111111 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 1.166666667x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 1.166666667x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 1.166666667x + x2 = 0 + -0.1111111111 1.166666667x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 1.166666667x + x2 = -0.1111111111 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 = -0.1111111111 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = -0.1111111111 + 0.3402777780 Combine like terms: -0.1111111111 + 0.3402777780 = 0.2291666669 0.3402777780 + 1.166666667x + x2 = 0.2291666669 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 0.2291666669 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 0.478713554 and -0.478713554.Subproblem 1
x + 0.5833333335 = 0.478713554 Simplifying x + 0.5833333335 = 0.478713554 Reorder the terms: 0.5833333335 + x = 0.478713554 Solving 0.5833333335 + x = 0.478713554 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 = 0.478713554 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 0.478713554 + -0.5833333335 x = 0.478713554 + -0.5833333335 Combine like terms: 0.478713554 + -0.5833333335 = -0.1046197795 x = -0.1046197795 Simplifying x = -0.1046197795Subproblem 2
x + 0.5833333335 = -0.478713554 Simplifying x + 0.5833333335 = -0.478713554 Reorder the terms: 0.5833333335 + x = -0.478713554 Solving 0.5833333335 + x = -0.478713554 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 = -0.478713554 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -0.478713554 + -0.5833333335 x = -0.478713554 + -0.5833333335 Combine like terms: -0.478713554 + -0.5833333335 = -1.0620468875 x = -1.0620468875 Simplifying x = -1.0620468875Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1046197795, -1.0620468875}
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