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Simplifying x2 + 24x + -38 = 0 Reorder the terms: -38 + 24x + x2 = 0 Solving -38 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 24x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 24x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 24x + x2 = 0 + 38 24x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 24x + x2 = 38 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 = 38 + 144 Reorder the terms: 144 + 24x + x2 = 38 + 144 Combine like terms: 38 + 144 = 182 144 + 24x + x2 = 182 Factor a perfect square on the left side: (x + 12)(x + 12) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (x + 12) equal to 13.490737563 and -13.490737563.Subproblem 1
x + 12 = 13.490737563 Simplifying x + 12 = 13.490737563 Reorder the terms: 12 + x = 13.490737563 Solving 12 + x = 13.490737563 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 = 13.490737563 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.490737563 + -12 x = 13.490737563 + -12 Combine like terms: 13.490737563 + -12 = 1.490737563 x = 1.490737563 Simplifying x = 1.490737563Subproblem 2
x + 12 = -13.490737563 Simplifying x + 12 = -13.490737563 Reorder the terms: 12 + x = -13.490737563 Solving 12 + x = -13.490737563 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 = -13.490737563 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.490737563 + -12 x = -13.490737563 + -12 Combine like terms: -13.490737563 + -12 = -25.490737563 x = -25.490737563 Simplifying x = -25.490737563Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.490737563, -25.490737563}
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