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Simplifying 0 = x2 + 12x + -478 Reorder the terms: 0 = -478 + 12x + x2 Solving 0 = -478 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + 478 = 478 478 + -12x + -1x2 = -478 + 12x + x2 + 478 + -12x + -1x2 Reorder the terms: 478 + -12x + -1x2 = -478 + 478 + 12x + -12x + x2 + -1x2 Combine like terms: -478 + 478 = 0 478 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 478 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 478 + -12x + -1x2 = 0 + x2 + -1x2 478 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 478 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -478 + 12x + x2 = 0 Move the constant term to the right: Add '478' to each side of the equation. -478 + 12x + 478 + x2 = 0 + 478 Reorder the terms: -478 + 478 + 12x + x2 = 0 + 478 Combine like terms: -478 + 478 = 0 0 + 12x + x2 = 0 + 478 12x + x2 = 0 + 478 Combine like terms: 0 + 478 = 478 12x + x2 = 478 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 = 478 + 36 Reorder the terms: 36 + 12x + x2 = 478 + 36 Combine like terms: 478 + 36 = 514 36 + 12x + x2 = 514 Factor a perfect square on the left side: (x + 6)(x + 6) = 514 Calculate the square root of the right side: 22.671568098 Break this problem into two subproblems by setting (x + 6) equal to 22.671568098 and -22.671568098.Subproblem 1
x + 6 = 22.671568098 Simplifying x + 6 = 22.671568098 Reorder the terms: 6 + x = 22.671568098 Solving 6 + x = 22.671568098 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 = 22.671568098 + -6 Combine like terms: 6 + -6 = 0 0 + x = 22.671568098 + -6 x = 22.671568098 + -6 Combine like terms: 22.671568098 + -6 = 16.671568098 x = 16.671568098 Simplifying x = 16.671568098Subproblem 2
x + 6 = -22.671568098 Simplifying x + 6 = -22.671568098 Reorder the terms: 6 + x = -22.671568098 Solving 6 + x = -22.671568098 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 = -22.671568098 + -6 Combine like terms: 6 + -6 = 0 0 + x = -22.671568098 + -6 x = -22.671568098 + -6 Combine like terms: -22.671568098 + -6 = -28.671568098 x = -28.671568098 Simplifying x = -28.671568098Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.671568098, -28.671568098}
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