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Simplifying x2 + 12x + -148 = 0 Reorder the terms: -148 + 12x + x2 = 0 Solving -148 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '148' to each side of the equation. -148 + 12x + 148 + x2 = 0 + 148 Reorder the terms: -148 + 148 + 12x + x2 = 0 + 148 Combine like terms: -148 + 148 = 0 0 + 12x + x2 = 0 + 148 12x + x2 = 0 + 148 Combine like terms: 0 + 148 = 148 12x + x2 = 148 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 = 148 + 36 Reorder the terms: 36 + 12x + x2 = 148 + 36 Combine like terms: 148 + 36 = 184 36 + 12x + x2 = 184 Factor a perfect square on the left side: (x + 6)(x + 6) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + 6) equal to 13.564659966 and -13.564659966.Subproblem 1
x + 6 = 13.564659966 Simplifying x + 6 = 13.564659966 Reorder the terms: 6 + x = 13.564659966 Solving 6 + x = 13.564659966 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 = 13.564659966 + -6 Combine like terms: 6 + -6 = 0 0 + x = 13.564659966 + -6 x = 13.564659966 + -6 Combine like terms: 13.564659966 + -6 = 7.564659966 x = 7.564659966 Simplifying x = 7.564659966Subproblem 2
x + 6 = -13.564659966 Simplifying x + 6 = -13.564659966 Reorder the terms: 6 + x = -13.564659966 Solving 6 + x = -13.564659966 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 = -13.564659966 + -6 Combine like terms: 6 + -6 = 0 0 + x = -13.564659966 + -6 x = -13.564659966 + -6 Combine like terms: -13.564659966 + -6 = -19.564659966 x = -19.564659966 Simplifying x = -19.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.564659966, -19.564659966}
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