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Simplifying 16x + 9 + x2 = 40000 Reorder the terms: 9 + 16x + x2 = 40000 Solving 9 + 16x + x2 = 40000 Solving for variable 'x'. Reorder the terms: 9 + -40000 + 16x + x2 = 40000 + -40000 Combine like terms: 9 + -40000 = -39991 -39991 + 16x + x2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -39991 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39991' to each side of the equation. -39991 + 16x + 39991 + x2 = 0 + 39991 Reorder the terms: -39991 + 39991 + 16x + x2 = 0 + 39991 Combine like terms: -39991 + 39991 = 0 0 + 16x + x2 = 0 + 39991 16x + x2 = 0 + 39991 Combine like terms: 0 + 39991 = 39991 16x + x2 = 39991 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 39991 + 64 Reorder the terms: 64 + 16x + x2 = 39991 + 64 Combine like terms: 39991 + 64 = 40055 64 + 16x + x2 = 40055 Factor a perfect square on the left side: (x + 8)(x + 8) = 40055 Calculate the square root of the right side: 200.137452767 Break this problem into two subproblems by setting (x + 8) equal to 200.137452767 and -200.137452767.Subproblem 1
x + 8 = 200.137452767 Simplifying x + 8 = 200.137452767 Reorder the terms: 8 + x = 200.137452767 Solving 8 + x = 200.137452767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 200.137452767 + -8 Combine like terms: 8 + -8 = 0 0 + x = 200.137452767 + -8 x = 200.137452767 + -8 Combine like terms: 200.137452767 + -8 = 192.137452767 x = 192.137452767 Simplifying x = 192.137452767Subproblem 2
x + 8 = -200.137452767 Simplifying x + 8 = -200.137452767 Reorder the terms: 8 + x = -200.137452767 Solving 8 + x = -200.137452767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -200.137452767 + -8 Combine like terms: 8 + -8 = 0 0 + x = -200.137452767 + -8 x = -200.137452767 + -8 Combine like terms: -200.137452767 + -8 = -208.137452767 x = -208.137452767 Simplifying x = -208.137452767Solution
The solution to the problem is based on the solutions from the subproblems. x = {192.137452767, -208.137452767}
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