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Simplifying x2 + 24x + 27 = 0 Reorder the terms: 27 + 24x + x2 = 0 Solving 27 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 24x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 24x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 24x + x2 = 0 + -27 24x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 24x + x2 = -27 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -27 + 144 Reorder the terms: 144 + 24x + x2 = -27 + 144 Combine like terms: -27 + 144 = 117 144 + 24x + x2 = 117 Factor a perfect square on the left side: (x + 12)(x + 12) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + 12) equal to 10.816653826 and -10.816653826.Subproblem 1
x + 12 = 10.816653826 Simplifying x + 12 = 10.816653826 Reorder the terms: 12 + x = 10.816653826 Solving 12 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 10.816653826 + -12 Combine like terms: 12 + -12 = 0 0 + x = 10.816653826 + -12 x = 10.816653826 + -12 Combine like terms: 10.816653826 + -12 = -1.183346174 x = -1.183346174 Simplifying x = -1.183346174Subproblem 2
x + 12 = -10.816653826 Simplifying x + 12 = -10.816653826 Reorder the terms: 12 + x = -10.816653826 Solving 12 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -10.816653826 + -12 Combine like terms: 12 + -12 = 0 0 + x = -10.816653826 + -12 x = -10.816653826 + -12 Combine like terms: -10.816653826 + -12 = -22.816653826 x = -22.816653826 Simplifying x = -22.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.183346174, -22.816653826}
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