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Simplifying 119 = (x + 3)(x + 6) Reorder the terms: 119 = (3 + x)(x + 6) Reorder the terms: 119 = (3 + x)(6 + x) Multiply (3 + x) * (6 + x) 119 = (3(6 + x) + x(6 + x)) 119 = ((6 * 3 + x * 3) + x(6 + x)) 119 = ((18 + 3x) + x(6 + x)) 119 = (18 + 3x + (6 * x + x * x)) 119 = (18 + 3x + (6x + x2)) Combine like terms: 3x + 6x = 9x 119 = (18 + 9x + x2) Solving 119 = 18 + 9x + x2 Solving for variable 'x'. Combine like terms: 119 + -18 = 101 101 + -9x + -1x2 = 18 + 9x + x2 + -18 + -9x + -1x2 Reorder the terms: 101 + -9x + -1x2 = 18 + -18 + 9x + -9x + x2 + -1x2 Combine like terms: 18 + -18 = 0 101 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2 101 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 101 + -9x + -1x2 = 0 + x2 + -1x2 101 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 101 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -101 + 9x + x2 = 0 Move the constant term to the right: Add '101' to each side of the equation. -101 + 9x + 101 + x2 = 0 + 101 Reorder the terms: -101 + 101 + 9x + x2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + 9x + x2 = 0 + 101 9x + x2 = 0 + 101 Combine like terms: 0 + 101 = 101 9x + x2 = 101 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 101 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 101 + 20.25 Combine like terms: 101 + 20.25 = 121.25 20.25 + 9x + x2 = 121.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (x + 4.5) equal to 11.011357773 and -11.011357773.Subproblem 1
x + 4.5 = 11.011357773 Simplifying x + 4.5 = 11.011357773 Reorder the terms: 4.5 + x = 11.011357773 Solving 4.5 + x = 11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 11.011357773 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.011357773 + -4.5 x = 11.011357773 + -4.5 Combine like terms: 11.011357773 + -4.5 = 6.511357773 x = 6.511357773 Simplifying x = 6.511357773Subproblem 2
x + 4.5 = -11.011357773 Simplifying x + 4.5 = -11.011357773 Reorder the terms: 4.5 + x = -11.011357773 Solving 4.5 + x = -11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -11.011357773 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.011357773 + -4.5 x = -11.011357773 + -4.5 Combine like terms: -11.011357773 + -4.5 = -15.511357773 x = -15.511357773 Simplifying x = -15.511357773Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.511357773, -15.511357773}
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