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Simplifying 6x2 + -7x + -222 = 0 Reorder the terms: -222 + -7x + 6x2 = 0 Solving -222 + -7x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -37 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -1.166666667x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -1.166666667x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -1.166666667x + x2 = 0 + 37 -1.166666667x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -1.166666667x + x2 = 37 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 = 37 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 37 + 0.3402777780 Combine like terms: 37 + 0.3402777780 = 37.340277778 0.3402777780 + -1.166666667x + x2 = 37.340277778 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 37.340277778 Calculate the square root of the right side: 6.110669176 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 6.110669176 and -6.110669176.Subproblem 1
x + -0.5833333335 = 6.110669176 Simplifying x + -0.5833333335 = 6.110669176 Reorder the terms: -0.5833333335 + x = 6.110669176 Solving -0.5833333335 + x = 6.110669176 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 = 6.110669176 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 6.110669176 + 0.5833333335 x = 6.110669176 + 0.5833333335 Combine like terms: 6.110669176 + 0.5833333335 = 6.6940025095 x = 6.6940025095 Simplifying x = 6.6940025095Subproblem 2
x + -0.5833333335 = -6.110669176 Simplifying x + -0.5833333335 = -6.110669176 Reorder the terms: -0.5833333335 + x = -6.110669176 Solving -0.5833333335 + x = -6.110669176 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 = -6.110669176 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -6.110669176 + 0.5833333335 x = -6.110669176 + 0.5833333335 Combine like terms: -6.110669176 + 0.5833333335 = -5.5273358425 x = -5.5273358425 Simplifying x = -5.5273358425Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6940025095, -5.5273358425}
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