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Simplifying x2 + -24x + 124 = 0 Reorder the terms: 124 + -24x + x2 = 0 Solving 124 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + -24x + -124 + x2 = 0 + -124 Reorder the terms: 124 + -124 + -24x + x2 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + -24x + x2 = 0 + -124 -24x + x2 = 0 + -124 Combine like terms: 0 + -124 = -124 -24x + x2 = -124 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 = -124 + 144 Reorder the terms: 144 + -24x + x2 = -124 + 144 Combine like terms: -124 + 144 = 20 144 + -24x + x2 = 20 Factor a perfect square on the left side: (x + -12)(x + -12) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -12) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -12 = 4.472135955 Simplifying x + -12 = 4.472135955 Reorder the terms: -12 + x = 4.472135955 Solving -12 + x = 4.472135955 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 = 4.472135955 + 12 Combine like terms: -12 + 12 = 0 0 + x = 4.472135955 + 12 x = 4.472135955 + 12 Combine like terms: 4.472135955 + 12 = 16.472135955 x = 16.472135955 Simplifying x = 16.472135955Subproblem 2
x + -12 = -4.472135955 Simplifying x + -12 = -4.472135955 Reorder the terms: -12 + x = -4.472135955 Solving -12 + x = -4.472135955 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 = -4.472135955 + 12 Combine like terms: -12 + 12 = 0 0 + x = -4.472135955 + 12 x = -4.472135955 + 12 Combine like terms: -4.472135955 + 12 = 7.527864045 x = 7.527864045 Simplifying x = 7.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.472135955, 7.527864045}
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