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Simplifying 9x(x + 12) = -13 Reorder the terms: 9x(12 + x) = -13 (12 * 9x + x * 9x) = -13 (108x + 9x2) = -13 Solving 108x + 9x2 = -13 Solving for variable 'x'. Reorder the terms: 13 + 108x + 9x2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + 108x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.444444444 + 12x + x2 = 0 Move the constant term to the right: Add '-1.444444444' to each side of the equation. 1.444444444 + 12x + -1.444444444 + x2 = 0 + -1.444444444 Reorder the terms: 1.444444444 + -1.444444444 + 12x + x2 = 0 + -1.444444444 Combine like terms: 1.444444444 + -1.444444444 = 0.000000000 0.000000000 + 12x + x2 = 0 + -1.444444444 12x + x2 = 0 + -1.444444444 Combine like terms: 0 + -1.444444444 = -1.444444444 12x + x2 = -1.444444444 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -1.444444444 + 36 Reorder the terms: 36 + 12x + x2 = -1.444444444 + 36 Combine like terms: -1.444444444 + 36 = 34.555555556 36 + 12x + x2 = 34.555555556 Factor a perfect square on the left side: (x + 6)(x + 6) = 34.555555556 Calculate the square root of the right side: 5.878397363 Break this problem into two subproblems by setting (x + 6) equal to 5.878397363 and -5.878397363.Subproblem 1
x + 6 = 5.878397363 Simplifying x + 6 = 5.878397363 Reorder the terms: 6 + x = 5.878397363 Solving 6 + x = 5.878397363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.878397363 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.878397363 + -6 x = 5.878397363 + -6 Combine like terms: 5.878397363 + -6 = -0.121602637 x = -0.121602637 Simplifying x = -0.121602637Subproblem 2
x + 6 = -5.878397363 Simplifying x + 6 = -5.878397363 Reorder the terms: 6 + x = -5.878397363 Solving 6 + x = -5.878397363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.878397363 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.878397363 + -6 x = -5.878397363 + -6 Combine like terms: -5.878397363 + -6 = -11.878397363 x = -11.878397363 Simplifying x = -11.878397363Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.121602637, -11.878397363}
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