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Simplifying x2 + 6x + -308 = 0 Reorder the terms: -308 + 6x + x2 = 0 Solving -308 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '308' to each side of the equation. -308 + 6x + 308 + x2 = 0 + 308 Reorder the terms: -308 + 308 + 6x + x2 = 0 + 308 Combine like terms: -308 + 308 = 0 0 + 6x + x2 = 0 + 308 6x + x2 = 0 + 308 Combine like terms: 0 + 308 = 308 6x + x2 = 308 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 = 308 + 9 Reorder the terms: 9 + 6x + x2 = 308 + 9 Combine like terms: 308 + 9 = 317 9 + 6x + x2 = 317 Factor a perfect square on the left side: (x + 3)(x + 3) = 317 Calculate the square root of the right side: 17.804493815 Break this problem into two subproblems by setting (x + 3) equal to 17.804493815 and -17.804493815.Subproblem 1
x + 3 = 17.804493815 Simplifying x + 3 = 17.804493815 Reorder the terms: 3 + x = 17.804493815 Solving 3 + x = 17.804493815 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 = 17.804493815 + -3 Combine like terms: 3 + -3 = 0 0 + x = 17.804493815 + -3 x = 17.804493815 + -3 Combine like terms: 17.804493815 + -3 = 14.804493815 x = 14.804493815 Simplifying x = 14.804493815Subproblem 2
x + 3 = -17.804493815 Simplifying x + 3 = -17.804493815 Reorder the terms: 3 + x = -17.804493815 Solving 3 + x = -17.804493815 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 = -17.804493815 + -3 Combine like terms: 3 + -3 = 0 0 + x = -17.804493815 + -3 x = -17.804493815 + -3 Combine like terms: -17.804493815 + -3 = -20.804493815 x = -20.804493815 Simplifying x = -20.804493815Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.804493815, -20.804493815}
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