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Simplifying x2 + 40x + 224 = 0 Reorder the terms: 224 + 40x + x2 = 0 Solving 224 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-224' to each side of the equation. 224 + 40x + -224 + x2 = 0 + -224 Reorder the terms: 224 + -224 + 40x + x2 = 0 + -224 Combine like terms: 224 + -224 = 0 0 + 40x + x2 = 0 + -224 40x + x2 = 0 + -224 Combine like terms: 0 + -224 = -224 40x + x2 = -224 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -224 + 400 Reorder the terms: 400 + 40x + x2 = -224 + 400 Combine like terms: -224 + 400 = 176 400 + 40x + x2 = 176 Factor a perfect square on the left side: (x + 20)(x + 20) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + 20) equal to 13.266499161 and -13.266499161.Subproblem 1
x + 20 = 13.266499161 Simplifying x + 20 = 13.266499161 Reorder the terms: 20 + x = 13.266499161 Solving 20 + x = 13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 13.266499161 + -20 Combine like terms: 20 + -20 = 0 0 + x = 13.266499161 + -20 x = 13.266499161 + -20 Combine like terms: 13.266499161 + -20 = -6.733500839 x = -6.733500839 Simplifying x = -6.733500839Subproblem 2
x + 20 = -13.266499161 Simplifying x + 20 = -13.266499161 Reorder the terms: 20 + x = -13.266499161 Solving 20 + x = -13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -13.266499161 + -20 Combine like terms: 20 + -20 = 0 0 + x = -13.266499161 + -20 x = -13.266499161 + -20 Combine like terms: -13.266499161 + -20 = -33.266499161 x = -33.266499161 Simplifying x = -33.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.733500839, -33.266499161}
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