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Simplifying (16 + -1x) + x(12 + -1x) = 18 Remove parenthesis around (16 + -1x) 16 + -1x + x(12 + -1x) = 18 16 + -1x + (12 * x + -1x * x) = 18 16 + -1x + (12x + -1x2) = 18 Combine like terms: -1x + 12x = 11x 16 + 11x + -1x2 = 18 Solving 16 + 11x + -1x2 = 18 Solving for variable 'x'. Reorder the terms: 16 + -18 + 11x + -1x2 = 18 + -18 Combine like terms: 16 + -18 = -2 -2 + 11x + -1x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -2 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -11x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -11x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -11x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -11x + x2 = 0 + -2 -11x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -11x + x2 = -2 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -2 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -2 + 30.25 Combine like terms: -2 + 30.25 = 28.25 30.25 + -11x + x2 = 28.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -5.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -5.5 = 5.315072906 Simplifying x + -5.5 = 5.315072906 Reorder the terms: -5.5 + x = 5.315072906 Solving -5.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.315072906 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.315072906 + 5.5 x = 5.315072906 + 5.5 Combine like terms: 5.315072906 + 5.5 = 10.815072906 x = 10.815072906 Simplifying x = 10.815072906Subproblem 2
x + -5.5 = -5.315072906 Simplifying x + -5.5 = -5.315072906 Reorder the terms: -5.5 + x = -5.315072906 Solving -5.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.315072906 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.315072906 + 5.5 x = -5.315072906 + 5.5 Combine like terms: -5.315072906 + 5.5 = 0.184927094 x = 0.184927094 Simplifying x = 0.184927094Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.815072906, 0.184927094}
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