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Simplifying x2 + 24x + 103 = 0 Reorder the terms: 103 + 24x + x2 = 0 Solving 103 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-103' to each side of the equation. 103 + 24x + -103 + x2 = 0 + -103 Reorder the terms: 103 + -103 + 24x + x2 = 0 + -103 Combine like terms: 103 + -103 = 0 0 + 24x + x2 = 0 + -103 24x + x2 = 0 + -103 Combine like terms: 0 + -103 = -103 24x + x2 = -103 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 = -103 + 144 Reorder the terms: 144 + 24x + x2 = -103 + 144 Combine like terms: -103 + 144 = 41 144 + 24x + x2 = 41 Factor a perfect square on the left side: (x + 12)(x + 12) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 12) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 12 = 6.403124237 Simplifying x + 12 = 6.403124237 Reorder the terms: 12 + x = 6.403124237 Solving 12 + x = 6.403124237 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 = 6.403124237 + -12 Combine like terms: 12 + -12 = 0 0 + x = 6.403124237 + -12 x = 6.403124237 + -12 Combine like terms: 6.403124237 + -12 = -5.596875763 x = -5.596875763 Simplifying x = -5.596875763Subproblem 2
x + 12 = -6.403124237 Simplifying x + 12 = -6.403124237 Reorder the terms: 12 + x = -6.403124237 Solving 12 + x = -6.403124237 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 = -6.403124237 + -12 Combine like terms: 12 + -12 = 0 0 + x = -6.403124237 + -12 x = -6.403124237 + -12 Combine like terms: -6.403124237 + -12 = -18.403124237 x = -18.403124237 Simplifying x = -18.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.596875763, -18.403124237}
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