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Simplifying x2 + 12x = -24 Reorder the terms: 12x + x2 = -24 Solving 12x + x2 = -24 Solving for variable 'x'. Reorder the terms: 24 + 12x + x2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 12x + x2 = 0 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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