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Simplifying (X + 6)(X + 6) = 21 Reorder the terms: (6 + X)(X + 6) = 21 Reorder the terms: (6 + X)(6 + X) = 21 Multiply (6 + X) * (6 + X) (6(6 + X) + X(6 + X)) = 21 ((6 * 6 + X * 6) + X(6 + X)) = 21 ((36 + 6X) + X(6 + X)) = 21 (36 + 6X + (6 * X + X * X)) = 21 (36 + 6X + (6X + X2)) = 21 Combine like terms: 6X + 6X = 12X (36 + 12X + X2) = 21 Solving 36 + 12X + X2 = 21 Solving for variable 'X'. Reorder the terms: 36 + -21 + 12X + X2 = 21 + -21 Combine like terms: 36 + -21 = 15 15 + 12X + X2 = 21 + -21 Combine like terms: 21 + -21 = 0 15 + 12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 12X + -15 + X2 = 0 + -15 Reorder the terms: 15 + -15 + 12X + X2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 12X + X2 = 0 + -15 12X + X2 = 0 + -15 Combine like terms: 0 + -15 = -15 12X + X2 = -15 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 = -15 + 36 Reorder the terms: 36 + 12X + X2 = -15 + 36 Combine like terms: -15 + 36 = 21 36 + 12X + X2 = 21 Factor a perfect square on the left side: (X + 6)(X + 6) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (X + 6) equal to 4.582575695 and -4.582575695.Subproblem 1
X + 6 = 4.582575695 Simplifying X + 6 = 4.582575695 Reorder the terms: 6 + X = 4.582575695 Solving 6 + X = 4.582575695 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 = 4.582575695 + -6 Combine like terms: 6 + -6 = 0 0 + X = 4.582575695 + -6 X = 4.582575695 + -6 Combine like terms: 4.582575695 + -6 = -1.417424305 X = -1.417424305 Simplifying X = -1.417424305Subproblem 2
X + 6 = -4.582575695 Simplifying X + 6 = -4.582575695 Reorder the terms: 6 + X = -4.582575695 Solving 6 + X = -4.582575695 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 = -4.582575695 + -6 Combine like terms: 6 + -6 = 0 0 + X = -4.582575695 + -6 X = -4.582575695 + -6 Combine like terms: -4.582575695 + -6 = -10.582575695 X = -10.582575695 Simplifying X = -10.582575695Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.417424305, -10.582575695}
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