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Simplifying (12 + X) * X = 36 Reorder the terms for easier multiplication: X(12 + X) = 36 (12 * X + X * X) = 36 (12X + X2) = 36 Solving 12X + X2 = 36 Solving for variable 'X'. Reorder the terms: -36 + 12X + X2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 12X + X2 = 0 Begin completing the square. 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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