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Simplifying x2 + 24x = 50 Reorder the terms: 24x + x2 = 50 Solving 24x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 24x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 24x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 24x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 24x + x2 = 0 + 50 24x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 24x + x2 = 50 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 = 50 + 144 Reorder the terms: 144 + 24x + x2 = 50 + 144 Combine like terms: 50 + 144 = 194 144 + 24x + x2 = 194 Factor a perfect square on the left side: (x + 12)(x + 12) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (x + 12) equal to 13.928388277 and -13.928388277.Subproblem 1
x + 12 = 13.928388277 Simplifying x + 12 = 13.928388277 Reorder the terms: 12 + x = 13.928388277 Solving 12 + x = 13.928388277 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 = 13.928388277 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.928388277 + -12 x = 13.928388277 + -12 Combine like terms: 13.928388277 + -12 = 1.928388277 x = 1.928388277 Simplifying x = 1.928388277Subproblem 2
x + 12 = -13.928388277 Simplifying x + 12 = -13.928388277 Reorder the terms: 12 + x = -13.928388277 Solving 12 + x = -13.928388277 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 = -13.928388277 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.928388277 + -12 x = -13.928388277 + -12 Combine like terms: -13.928388277 + -12 = -25.928388277 x = -25.928388277 Simplifying x = -25.928388277Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.928388277, -25.928388277}
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