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Simplifying -0.83x2 + 12x + -18 = 0 Reorder the terms: -18 + 12x + -0.83x2 = 0 Solving -18 + 12x + -0.83x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.83 the coefficient of the squared term: Divide each side by '-0.83'. 21.68674699 + -14.45783133x + x2 = 0 Move the constant term to the right: Add '-21.68674699' to each side of the equation. 21.68674699 + -14.45783133x + -21.68674699 + x2 = 0 + -21.68674699 Reorder the terms: 21.68674699 + -21.68674699 + -14.45783133x + x2 = 0 + -21.68674699 Combine like terms: 21.68674699 + -21.68674699 = 0.00000000 0.00000000 + -14.45783133x + x2 = 0 + -21.68674699 -14.45783133x + x2 = 0 + -21.68674699 Combine like terms: 0 + -21.68674699 = -21.68674699 -14.45783133x + x2 = -21.68674699 The x term is -14.45783133x. Take half its coefficient (-7.228915665). Square it (52.25722169) and add it to both sides. Add '52.25722169' to each side of the equation. -14.45783133x + 52.25722169 + x2 = -21.68674699 + 52.25722169 Reorder the terms: 52.25722169 + -14.45783133x + x2 = -21.68674699 + 52.25722169 Combine like terms: -21.68674699 + 52.25722169 = 30.5704747 52.25722169 + -14.45783133x + x2 = 30.5704747 Factor a perfect square on the left side: (x + -7.228915665)(x + -7.228915665) = 30.5704747 Calculate the square root of the right side: 5.529057307 Break this problem into two subproblems by setting (x + -7.228915665) equal to 5.529057307 and -5.529057307.Subproblem 1
x + -7.228915665 = 5.529057307 Simplifying x + -7.228915665 = 5.529057307 Reorder the terms: -7.228915665 + x = 5.529057307 Solving -7.228915665 + x = 5.529057307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.228915665' to each side of the equation. -7.228915665 + 7.228915665 + x = 5.529057307 + 7.228915665 Combine like terms: -7.228915665 + 7.228915665 = 0.000000000 0.000000000 + x = 5.529057307 + 7.228915665 x = 5.529057307 + 7.228915665 Combine like terms: 5.529057307 + 7.228915665 = 12.757972972 x = 12.757972972 Simplifying x = 12.757972972Subproblem 2
x + -7.228915665 = -5.529057307 Simplifying x + -7.228915665 = -5.529057307 Reorder the terms: -7.228915665 + x = -5.529057307 Solving -7.228915665 + x = -5.529057307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.228915665' to each side of the equation. -7.228915665 + 7.228915665 + x = -5.529057307 + 7.228915665 Combine like terms: -7.228915665 + 7.228915665 = 0.000000000 0.000000000 + x = -5.529057307 + 7.228915665 x = -5.529057307 + 7.228915665 Combine like terms: -5.529057307 + 7.228915665 = 1.699858358 x = 1.699858358 Simplifying x = 1.699858358Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.757972972, 1.699858358}
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