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Simplifying x2 + 12x = -28 Reorder the terms: 12x + x2 = -28 Solving 12x + x2 = -28 Solving for variable 'x'. Reorder the terms: 28 + 12x + x2 = -28 + 28 Combine like terms: -28 + 28 = 0 28 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 12x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + 12x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 12x + x2 = 0 + -28 12x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 12x + x2 = -28 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 = -28 + 36 Reorder the terms: 36 + 12x + x2 = -28 + 36 Combine like terms: -28 + 36 = 8 36 + 12x + x2 = 8 Factor a perfect square on the left side: (x + 6)(x + 6) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 6) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 6 = 2.828427125 Simplifying x + 6 = 2.828427125 Reorder the terms: 6 + x = 2.828427125 Solving 6 + x = 2.828427125 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 = 2.828427125 + -6 Combine like terms: 6 + -6 = 0 0 + x = 2.828427125 + -6 x = 2.828427125 + -6 Combine like terms: 2.828427125 + -6 = -3.171572875 x = -3.171572875 Simplifying x = -3.171572875Subproblem 2
x + 6 = -2.828427125 Simplifying x + 6 = -2.828427125 Reorder the terms: 6 + x = -2.828427125 Solving 6 + x = -2.828427125 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 = -2.828427125 + -6 Combine like terms: 6 + -6 = 0 0 + x = -2.828427125 + -6 x = -2.828427125 + -6 Combine like terms: -2.828427125 + -6 = -8.828427125 x = -8.828427125 Simplifying x = -8.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.171572875, -8.828427125}
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