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Simplifying x2 + 24x = 32 Reorder the terms: 24x + x2 = 32 Solving 24x + x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 24x + x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 24x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 24x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 24x + x2 = 0 + 32 24x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 24x + x2 = 32 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 = 32 + 144 Reorder the terms: 144 + 24x + x2 = 32 + 144 Combine like terms: 32 + 144 = 176 144 + 24x + x2 = 176 Factor a perfect square on the left side: (x + 12)(x + 12) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + 12) equal to 13.266499161 and -13.266499161.Subproblem 1
x + 12 = 13.266499161 Simplifying x + 12 = 13.266499161 Reorder the terms: 12 + x = 13.266499161 Solving 12 + x = 13.266499161 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 = 13.266499161 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.266499161 + -12 x = 13.266499161 + -12 Combine like terms: 13.266499161 + -12 = 1.266499161 x = 1.266499161 Simplifying x = 1.266499161Subproblem 2
x + 12 = -13.266499161 Simplifying x + 12 = -13.266499161 Reorder the terms: 12 + x = -13.266499161 Solving 12 + x = -13.266499161 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 = -13.266499161 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.266499161 + -12 x = -13.266499161 + -12 Combine like terms: -13.266499161 + -12 = -25.266499161 x = -25.266499161 Simplifying x = -25.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.266499161, -25.266499161}
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