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Simplifying x(x + 6) = 110 Reorder the terms: x(6 + x) = 110 (6 * x + x * x) = 110 (6x + x2) = 110 Solving 6x + x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + 6x + x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 6x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 6x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 6x + x2 = 0 + 110 6x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 6x + x2 = 110 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 110 + 9 Reorder the terms: 9 + 6x + x2 = 110 + 9 Combine like terms: 110 + 9 = 119 9 + 6x + x2 = 119 Factor a perfect square on the left side: (x + 3)(x + 3) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + 3) equal to 10.908712115 and -10.908712115.Subproblem 1
x + 3 = 10.908712115 Simplifying x + 3 = 10.908712115 Reorder the terms: 3 + x = 10.908712115 Solving 3 + x = 10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 10.908712115 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.908712115 + -3 x = 10.908712115 + -3 Combine like terms: 10.908712115 + -3 = 7.908712115 x = 7.908712115 Simplifying x = 7.908712115Subproblem 2
x + 3 = -10.908712115 Simplifying x + 3 = -10.908712115 Reorder the terms: 3 + x = -10.908712115 Solving 3 + x = -10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -10.908712115 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.908712115 + -3 x = -10.908712115 + -3 Combine like terms: -10.908712115 + -3 = -13.908712115 x = -13.908712115 Simplifying x = -13.908712115Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.908712115, -13.908712115}
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