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Simplifying x2 + 28x + 12 = 0 Reorder the terms: 12 + 28x + x2 = 0 Solving 12 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 28x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 28x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 28x + x2 = 0 + -12 28x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 28x + x2 = -12 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -12 + 196 Reorder the terms: 196 + 28x + x2 = -12 + 196 Combine like terms: -12 + 196 = 184 196 + 28x + x2 = 184 Factor a perfect square on the left side: (x + 14)(x + 14) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + 14) equal to 13.564659966 and -13.564659966.Subproblem 1
x + 14 = 13.564659966 Simplifying x + 14 = 13.564659966 Reorder the terms: 14 + x = 13.564659966 Solving 14 + x = 13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 13.564659966 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.564659966 + -14 x = 13.564659966 + -14 Combine like terms: 13.564659966 + -14 = -0.435340034 x = -0.435340034 Simplifying x = -0.435340034Subproblem 2
x + 14 = -13.564659966 Simplifying x + 14 = -13.564659966 Reorder the terms: 14 + x = -13.564659966 Solving 14 + x = -13.564659966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -13.564659966 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.564659966 + -14 x = -13.564659966 + -14 Combine like terms: -13.564659966 + -14 = -27.564659966 x = -27.564659966 Simplifying x = -27.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.435340034, -27.564659966}
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