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Simplifying 36 = x(x + 12) Reorder the terms: 36 = x(12 + x) 36 = (12 * x + x * x) 36 = (12x + x2) Solving 36 = 12x + x2 Solving for variable 'x'. Reorder the terms: 36 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 36 + -12x + -1x2 = 0 + x2 + -1x2 36 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 12x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 12x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 12x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 12x + x2 = 0 + 36 12x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 12x + x2 = 36 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 = 36 + 36 Reorder the terms: 36 + 12x + x2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + 12x + x2 = 72 Factor a perfect square on the left side: (x + 6)(x + 6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + 6) equal to 8.485281374 and -8.485281374.Subproblem 1
x + 6 = 8.485281374 Simplifying x + 6 = 8.485281374 Reorder the terms: 6 + x = 8.485281374 Solving 6 + x = 8.485281374 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 = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.485281374 + -6 x = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 x = 2.485281374 Simplifying x = 2.485281374Subproblem 2
x + 6 = -8.485281374 Simplifying x + 6 = -8.485281374 Reorder the terms: 6 + x = -8.485281374 Solving 6 + x = -8.485281374 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 = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.485281374 + -6 x = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 x = -14.485281374 Simplifying x = -14.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.485281374, -14.485281374}
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