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Simplifying 0 = x2 + 12x + -352 Reorder the terms: 0 = -352 + 12x + x2 Solving 0 = -352 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + 352 = 352 352 + -12x + -1x2 = -352 + 12x + x2 + 352 + -12x + -1x2 Reorder the terms: 352 + -12x + -1x2 = -352 + 352 + 12x + -12x + x2 + -1x2 Combine like terms: -352 + 352 = 0 352 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 352 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 352 + -12x + -1x2 = 0 + x2 + -1x2 352 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 352 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -352 + 12x + x2 = 0 Move the constant term to the right: Add '352' to each side of the equation. -352 + 12x + 352 + x2 = 0 + 352 Reorder the terms: -352 + 352 + 12x + x2 = 0 + 352 Combine like terms: -352 + 352 = 0 0 + 12x + x2 = 0 + 352 12x + x2 = 0 + 352 Combine like terms: 0 + 352 = 352 12x + x2 = 352 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 = 352 + 36 Reorder the terms: 36 + 12x + x2 = 352 + 36 Combine like terms: 352 + 36 = 388 36 + 12x + x2 = 388 Factor a perfect square on the left side: (x + 6)(x + 6) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (x + 6) equal to 19.697715604 and -19.697715604.Subproblem 1
x + 6 = 19.697715604 Simplifying x + 6 = 19.697715604 Reorder the terms: 6 + x = 19.697715604 Solving 6 + x = 19.697715604 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 = 19.697715604 + -6 Combine like terms: 6 + -6 = 0 0 + x = 19.697715604 + -6 x = 19.697715604 + -6 Combine like terms: 19.697715604 + -6 = 13.697715604 x = 13.697715604 Simplifying x = 13.697715604Subproblem 2
x + 6 = -19.697715604 Simplifying x + 6 = -19.697715604 Reorder the terms: 6 + x = -19.697715604 Solving 6 + x = -19.697715604 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 = -19.697715604 + -6 Combine like terms: 6 + -6 = 0 0 + x = -19.697715604 + -6 x = -19.697715604 + -6 Combine like terms: -19.697715604 + -6 = -25.697715604 x = -25.697715604 Simplifying x = -25.697715604Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.697715604, -25.697715604}
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