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Simplifying x2 + 6x + -180 = 0 Reorder the terms: -180 + 6x + x2 = 0 Solving -180 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 6x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 6x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 6x + x2 = 0 + 180 6x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 6x + x2 = 180 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 = 180 + 9 Reorder the terms: 9 + 6x + x2 = 180 + 9 Combine like terms: 180 + 9 = 189 9 + 6x + x2 = 189 Factor a perfect square on the left side: (x + 3)(x + 3) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + 3) equal to 13.747727085 and -13.747727085.Subproblem 1
x + 3 = 13.747727085 Simplifying x + 3 = 13.747727085 Reorder the terms: 3 + x = 13.747727085 Solving 3 + x = 13.747727085 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 = 13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.747727085 + -3 x = 13.747727085 + -3 Combine like terms: 13.747727085 + -3 = 10.747727085 x = 10.747727085 Simplifying x = 10.747727085Subproblem 2
x + 3 = -13.747727085 Simplifying x + 3 = -13.747727085 Reorder the terms: 3 + x = -13.747727085 Solving 3 + x = -13.747727085 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 = -13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.747727085 + -3 x = -13.747727085 + -3 Combine like terms: -13.747727085 + -3 = -16.747727085 x = -16.747727085 Simplifying x = -16.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.747727085, -16.747727085}
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