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Simplifying x2 + 24x = 11 Reorder the terms: 24x + x2 = 11 Solving 24x + x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 24x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 24x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 24x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 24x + x2 = 0 + 11 24x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 24x + x2 = 11 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 = 11 + 144 Reorder the terms: 144 + 24x + x2 = 11 + 144 Combine like terms: 11 + 144 = 155 144 + 24x + x2 = 155 Factor a perfect square on the left side: (x + 12)(x + 12) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (x + 12) equal to 12.449899598 and -12.449899598.Subproblem 1
x + 12 = 12.449899598 Simplifying x + 12 = 12.449899598 Reorder the terms: 12 + x = 12.449899598 Solving 12 + x = 12.449899598 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 = 12.449899598 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.449899598 + -12 x = 12.449899598 + -12 Combine like terms: 12.449899598 + -12 = 0.449899598 x = 0.449899598 Simplifying x = 0.449899598Subproblem 2
x + 12 = -12.449899598 Simplifying x + 12 = -12.449899598 Reorder the terms: 12 + x = -12.449899598 Solving 12 + x = -12.449899598 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 = -12.449899598 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.449899598 + -12 x = -12.449899598 + -12 Combine like terms: -12.449899598 + -12 = -24.449899598 x = -24.449899598 Simplifying x = -24.449899598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.449899598, -24.449899598}
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