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Simplifying x2 + -24x + 105 = 0 Reorder the terms: 105 + -24x + x2 = 0 Solving 105 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-105' to each side of the equation. 105 + -24x + -105 + x2 = 0 + -105 Reorder the terms: 105 + -105 + -24x + x2 = 0 + -105 Combine like terms: 105 + -105 = 0 0 + -24x + x2 = 0 + -105 -24x + x2 = 0 + -105 Combine like terms: 0 + -105 = -105 -24x + x2 = -105 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 = -105 + 144 Reorder the terms: 144 + -24x + x2 = -105 + 144 Combine like terms: -105 + 144 = 39 144 + -24x + x2 = 39 Factor a perfect square on the left side: (x + -12)(x + -12) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -12) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -12 = 6.244997998 Simplifying x + -12 = 6.244997998 Reorder the terms: -12 + x = 6.244997998 Solving -12 + x = 6.244997998 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 = 6.244997998 + 12 Combine like terms: -12 + 12 = 0 0 + x = 6.244997998 + 12 x = 6.244997998 + 12 Combine like terms: 6.244997998 + 12 = 18.244997998 x = 18.244997998 Simplifying x = 18.244997998Subproblem 2
x + -12 = -6.244997998 Simplifying x + -12 = -6.244997998 Reorder the terms: -12 + x = -6.244997998 Solving -12 + x = -6.244997998 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 = -6.244997998 + 12 Combine like terms: -12 + 12 = 0 0 + x = -6.244997998 + 12 x = -6.244997998 + 12 Combine like terms: -6.244997998 + 12 = 5.755002002 x = 5.755002002 Simplifying x = 5.755002002Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.244997998, 5.755002002}
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