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Simplifying x2 + 24x + 144 = 29 Reorder the terms: 144 + 24x + x2 = 29 Solving 144 + 24x + x2 = 29 Solving for variable 'x'. Reorder the terms: 144 + -29 + 24x + x2 = 29 + -29 Combine like terms: 144 + -29 = 115 115 + 24x + x2 = 29 + -29 Combine like terms: 29 + -29 = 0 115 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-115' to each side of the equation. 115 + 24x + -115 + x2 = 0 + -115 Reorder the terms: 115 + -115 + 24x + x2 = 0 + -115 Combine like terms: 115 + -115 = 0 0 + 24x + x2 = 0 + -115 24x + x2 = 0 + -115 Combine like terms: 0 + -115 = -115 24x + x2 = -115 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 = -115 + 144 Reorder the terms: 144 + 24x + x2 = -115 + 144 Combine like terms: -115 + 144 = 29 144 + 24x + x2 = 29 Factor a perfect square on the left side: (x + 12)(x + 12) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 12) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 12 = 5.385164807 Simplifying x + 12 = 5.385164807 Reorder the terms: 12 + x = 5.385164807 Solving 12 + x = 5.385164807 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 = 5.385164807 + -12 Combine like terms: 12 + -12 = 0 0 + x = 5.385164807 + -12 x = 5.385164807 + -12 Combine like terms: 5.385164807 + -12 = -6.614835193 x = -6.614835193 Simplifying x = -6.614835193Subproblem 2
x + 12 = -5.385164807 Simplifying x + 12 = -5.385164807 Reorder the terms: 12 + x = -5.385164807 Solving 12 + x = -5.385164807 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 = -5.385164807 + -12 Combine like terms: 12 + -12 = 0 0 + x = -5.385164807 + -12 x = -5.385164807 + -12 Combine like terms: -5.385164807 + -12 = -17.385164807 x = -17.385164807 Simplifying x = -17.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.614835193, -17.385164807}
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