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Simplifying X2 + 1600 + 160X = 0 Reorder the terms: 1600 + 160X + X2 = 0 Solving 1600 + 160X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-1600' to each side of the equation. 1600 + 160X + -1600 + X2 = 0 + -1600 Reorder the terms: 1600 + -1600 + 160X + X2 = 0 + -1600 Combine like terms: 1600 + -1600 = 0 0 + 160X + X2 = 0 + -1600 160X + X2 = 0 + -1600 Combine like terms: 0 + -1600 = -1600 160X + X2 = -1600 The X term is 160X. Take half its coefficient (80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. 160X + 6400 + X2 = -1600 + 6400 Reorder the terms: 6400 + 160X + X2 = -1600 + 6400 Combine like terms: -1600 + 6400 = 4800 6400 + 160X + X2 = 4800 Factor a perfect square on the left side: (X + 80)(X + 80) = 4800 Calculate the square root of the right side: 69.282032303 Break this problem into two subproblems by setting (X + 80) equal to 69.282032303 and -69.282032303.Subproblem 1
X + 80 = 69.282032303 Simplifying X + 80 = 69.282032303 Reorder the terms: 80 + X = 69.282032303 Solving 80 + X = 69.282032303 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + X = 69.282032303 + -80 Combine like terms: 80 + -80 = 0 0 + X = 69.282032303 + -80 X = 69.282032303 + -80 Combine like terms: 69.282032303 + -80 = -10.717967697 X = -10.717967697 Simplifying X = -10.717967697Subproblem 2
X + 80 = -69.282032303 Simplifying X + 80 = -69.282032303 Reorder the terms: 80 + X = -69.282032303 Solving 80 + X = -69.282032303 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + X = -69.282032303 + -80 Combine like terms: 80 + -80 = 0 0 + X = -69.282032303 + -80 X = -69.282032303 + -80 Combine like terms: -69.282032303 + -80 = -149.282032303 X = -149.282032303 Simplifying X = -149.282032303Solution
The solution to the problem is based on the solutions from the subproblems. X = {-10.717967697, -149.282032303}
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