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Simplifying X(X + 12) = 400 Reorder the terms: X(12 + X) = 400 (12 * X + X * X) = 400 (12X + X2) = 400 Solving 12X + X2 = 400 Solving for variable 'X'. Reorder the terms: -400 + 12X + X2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 12X + 400 + X2 = 0 + 400 Reorder the terms: -400 + 400 + 12X + X2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 12X + X2 = 0 + 400 12X + X2 = 0 + 400 Combine like terms: 0 + 400 = 400 12X + X2 = 400 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 = 400 + 36 Reorder the terms: 36 + 12X + X2 = 400 + 36 Combine like terms: 400 + 36 = 436 36 + 12X + X2 = 436 Factor a perfect square on the left side: (X + 6)(X + 6) = 436 Calculate the square root of the right side: 20.880613018 Break this problem into two subproblems by setting (X + 6) equal to 20.880613018 and -20.880613018.Subproblem 1
X + 6 = 20.880613018 Simplifying X + 6 = 20.880613018 Reorder the terms: 6 + X = 20.880613018 Solving 6 + X = 20.880613018 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 = 20.880613018 + -6 Combine like terms: 6 + -6 = 0 0 + X = 20.880613018 + -6 X = 20.880613018 + -6 Combine like terms: 20.880613018 + -6 = 14.880613018 X = 14.880613018 Simplifying X = 14.880613018Subproblem 2
X + 6 = -20.880613018 Simplifying X + 6 = -20.880613018 Reorder the terms: 6 + X = -20.880613018 Solving 6 + X = -20.880613018 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 = -20.880613018 + -6 Combine like terms: 6 + -6 = 0 0 + X = -20.880613018 + -6 X = -20.880613018 + -6 Combine like terms: -20.880613018 + -6 = -26.880613018 X = -26.880613018 Simplifying X = -26.880613018Solution
The solution to the problem is based on the solutions from the subproblems. X = {14.880613018, -26.880613018}
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