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Simplifying X2 + 12X + 24 = 0 Reorder the terms: 24 + 12X + X2 = 0 Solving 24 + 12X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 12X + -24 + X2 = 0 + -24 Reorder the terms: 24 + -24 + 12X + X2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 12X + X2 = 0 + -24 12X + X2 = 0 + -24 Combine like terms: 0 + -24 = -24 12X + X2 = -24 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 = -24 + 36 Reorder the terms: 36 + 12X + X2 = -24 + 36 Combine like terms: -24 + 36 = 12 36 + 12X + X2 = 12 Factor a perfect square on the left side: (X + 6)(X + 6) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (X + 6) equal to 3.464101615 and -3.464101615.Subproblem 1
X + 6 = 3.464101615 Simplifying X + 6 = 3.464101615 Reorder the terms: 6 + X = 3.464101615 Solving 6 + X = 3.464101615 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 = 3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + X = 3.464101615 + -6 X = 3.464101615 + -6 Combine like terms: 3.464101615 + -6 = -2.535898385 X = -2.535898385 Simplifying X = -2.535898385Subproblem 2
X + 6 = -3.464101615 Simplifying X + 6 = -3.464101615 Reorder the terms: 6 + X = -3.464101615 Solving 6 + X = -3.464101615 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 = -3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + X = -3.464101615 + -6 X = -3.464101615 + -6 Combine like terms: -3.464101615 + -6 = -9.464101615 X = -9.464101615 Simplifying X = -9.464101615Solution
The solution to the problem is based on the solutions from the subproblems. X = {-2.535898385, -9.464101615}
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