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Simplifying [x2 + 6x + 8] + [x2 + 9x + 18] = 0 Reorder the terms: [8 + 6x + x2] + [x2 + 9x + 18] = 0 Remove brackets around [8 + 6x + x2] 8 + 6x + x2 + [x2 + 9x + 18] = 0 Reorder the terms: 8 + 6x + x2 + [18 + 9x + x2] = 0 Remove brackets around [18 + 9x + x2] 8 + 6x + x2 + 18 + 9x + x2 = 0 Reorder the terms: 8 + 18 + 6x + 9x + x2 + x2 = 0 Combine like terms: 8 + 18 = 26 26 + 6x + 9x + x2 + x2 = 0 Combine like terms: 6x + 9x = 15x 26 + 15x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 26 + 15x + 2x2 = 0 Solving 26 + 15x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13 + 7.5x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + 7.5x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 7.5x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 7.5x + x2 = 0 + -13 7.5x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 7.5x + x2 = -13 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -13 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -13 + 14.0625 Combine like terms: -13 + 14.0625 = 1.0625 14.0625 + 7.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 3.75) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 3.75 = 1.030776406 Simplifying x + 3.75 = 1.030776406 Reorder the terms: 3.75 + x = 1.030776406 Solving 3.75 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 1.030776406 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 1.030776406 + -3.75 x = 1.030776406 + -3.75 Combine like terms: 1.030776406 + -3.75 = -2.719223594 x = -2.719223594 Simplifying x = -2.719223594Subproblem 2
x + 3.75 = -1.030776406 Simplifying x + 3.75 = -1.030776406 Reorder the terms: 3.75 + x = -1.030776406 Solving 3.75 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -1.030776406 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -1.030776406 + -3.75 x = -1.030776406 + -3.75 Combine like terms: -1.030776406 + -3.75 = -4.780776406 x = -4.780776406 Simplifying x = -4.780776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.719223594, -4.780776406}
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