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Simplifying x2 + 160x + 1000 = 0 Reorder the terms: 1000 + 160x + x2 = 0 Solving 1000 + 160x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + 160x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + 160x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + 160x + x2 = 0 + -1000 160x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 160x + x2 = -1000 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 = -1000 + 6400 Reorder the terms: 6400 + 160x + x2 = -1000 + 6400 Combine like terms: -1000 + 6400 = 5400 6400 + 160x + x2 = 5400 Factor a perfect square on the left side: (x + 80)(x + 80) = 5400 Calculate the square root of the right side: 73.484692283 Break this problem into two subproblems by setting (x + 80) equal to 73.484692283 and -73.484692283.Subproblem 1
x + 80 = 73.484692283 Simplifying x + 80 = 73.484692283 Reorder the terms: 80 + x = 73.484692283 Solving 80 + x = 73.484692283 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 = 73.484692283 + -80 Combine like terms: 80 + -80 = 0 0 + x = 73.484692283 + -80 x = 73.484692283 + -80 Combine like terms: 73.484692283 + -80 = -6.515307717 x = -6.515307717 Simplifying x = -6.515307717Subproblem 2
x + 80 = -73.484692283 Simplifying x + 80 = -73.484692283 Reorder the terms: 80 + x = -73.484692283 Solving 80 + x = -73.484692283 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 = -73.484692283 + -80 Combine like terms: 80 + -80 = 0 0 + x = -73.484692283 + -80 x = -73.484692283 + -80 Combine like terms: -73.484692283 + -80 = -153.484692283 x = -153.484692283 Simplifying x = -153.484692283Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.515307717, -153.484692283}
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