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Simplifying x2 + 3x + 9x + -8 = 360 Reorder the terms: -8 + 3x + 9x + x2 = 360 Combine like terms: 3x + 9x = 12x -8 + 12x + x2 = 360 Solving -8 + 12x + x2 = 360 Solving for variable 'x'. Reorder the terms: -8 + -360 + 12x + x2 = 360 + -360 Combine like terms: -8 + -360 = -368 -368 + 12x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -368 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '368' to each side of the equation. -368 + 12x + 368 + x2 = 0 + 368 Reorder the terms: -368 + 368 + 12x + x2 = 0 + 368 Combine like terms: -368 + 368 = 0 0 + 12x + x2 = 0 + 368 12x + x2 = 0 + 368 Combine like terms: 0 + 368 = 368 12x + x2 = 368 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 = 368 + 36 Reorder the terms: 36 + 12x + x2 = 368 + 36 Combine like terms: 368 + 36 = 404 36 + 12x + x2 = 404 Factor a perfect square on the left side: (x + 6)(x + 6) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (x + 6) equal to 20.099751242 and -20.099751242.Subproblem 1
x + 6 = 20.099751242 Simplifying x + 6 = 20.099751242 Reorder the terms: 6 + x = 20.099751242 Solving 6 + x = 20.099751242 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 = 20.099751242 + -6 Combine like terms: 6 + -6 = 0 0 + x = 20.099751242 + -6 x = 20.099751242 + -6 Combine like terms: 20.099751242 + -6 = 14.099751242 x = 14.099751242 Simplifying x = 14.099751242Subproblem 2
x + 6 = -20.099751242 Simplifying x + 6 = -20.099751242 Reorder the terms: 6 + x = -20.099751242 Solving 6 + x = -20.099751242 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 = -20.099751242 + -6 Combine like terms: 6 + -6 = 0 0 + x = -20.099751242 + -6 x = -20.099751242 + -6 Combine like terms: -20.099751242 + -6 = -26.099751242 x = -26.099751242 Simplifying x = -26.099751242Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.099751242, -26.099751242}
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