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Simplifying 432 = x2 + 12x + 36 Reorder the terms: 432 = 36 + 12x + x2 Solving 432 = 36 + 12x + x2 Solving for variable 'x'. Combine like terms: 432 + -36 = 396 396 + -12x + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2 Reorder the terms: 396 + -12x + -1x2 = 36 + -36 + 12x + -12x + x2 + -1x2 Combine like terms: 36 + -36 = 0 396 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 396 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 396 + -12x + -1x2 = 0 + x2 + -1x2 396 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 396 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -396 + 12x + x2 = 0 Move the constant term to the right: Add '396' to each side of the equation. -396 + 12x + 396 + x2 = 0 + 396 Reorder the terms: -396 + 396 + 12x + x2 = 0 + 396 Combine like terms: -396 + 396 = 0 0 + 12x + x2 = 0 + 396 12x + x2 = 0 + 396 Combine like terms: 0 + 396 = 396 12x + x2 = 396 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 = 396 + 36 Reorder the terms: 36 + 12x + x2 = 396 + 36 Combine like terms: 396 + 36 = 432 36 + 12x + x2 = 432 Factor a perfect square on the left side: (x + 6)(x + 6) = 432 Calculate the square root of the right side: 20.784609691 Break this problem into two subproblems by setting (x + 6) equal to 20.784609691 and -20.784609691.Subproblem 1
x + 6 = 20.784609691 Simplifying x + 6 = 20.784609691 Reorder the terms: 6 + x = 20.784609691 Solving 6 + x = 20.784609691 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 = 20.784609691 + -6 Combine like terms: 6 + -6 = 0 0 + x = 20.784609691 + -6 x = 20.784609691 + -6 Combine like terms: 20.784609691 + -6 = 14.784609691 x = 14.784609691 Simplifying x = 14.784609691Subproblem 2
x + 6 = -20.784609691 Simplifying x + 6 = -20.784609691 Reorder the terms: 6 + x = -20.784609691 Solving 6 + x = -20.784609691 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 = -20.784609691 + -6 Combine like terms: 6 + -6 = 0 0 + x = -20.784609691 + -6 x = -20.784609691 + -6 Combine like terms: -20.784609691 + -6 = -26.784609691 x = -26.784609691 Simplifying x = -26.784609691Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.784609691, -26.784609691}
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