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Simplifying x2 + 12x + -196 = 0 Reorder the terms: -196 + 12x + x2 = 0 Solving -196 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 12x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 12x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 12x + x2 = 0 + 196 12x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 12x + x2 = 196 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 = 196 + 36 Reorder the terms: 36 + 12x + x2 = 196 + 36 Combine like terms: 196 + 36 = 232 36 + 12x + x2 = 232 Factor a perfect square on the left side: (x + 6)(x + 6) = 232 Calculate the square root of the right side: 15.231546212 Break this problem into two subproblems by setting (x + 6) equal to 15.231546212 and -15.231546212.Subproblem 1
x + 6 = 15.231546212 Simplifying x + 6 = 15.231546212 Reorder the terms: 6 + x = 15.231546212 Solving 6 + x = 15.231546212 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 = 15.231546212 + -6 Combine like terms: 6 + -6 = 0 0 + x = 15.231546212 + -6 x = 15.231546212 + -6 Combine like terms: 15.231546212 + -6 = 9.231546212 x = 9.231546212 Simplifying x = 9.231546212Subproblem 2
x + 6 = -15.231546212 Simplifying x + 6 = -15.231546212 Reorder the terms: 6 + x = -15.231546212 Solving 6 + x = -15.231546212 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 = -15.231546212 + -6 Combine like terms: 6 + -6 = 0 0 + x = -15.231546212 + -6 x = -15.231546212 + -6 Combine like terms: -15.231546212 + -6 = -21.231546212 x = -21.231546212 Simplifying x = -21.231546212Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.231546212, -21.231546212}
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