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Simplifying 0 = -1x2 + 160x + -1000 Reorder the terms: 0 = -1000 + 160x + -1x2 Solving 0 = -1000 + 160x + -1x2 Solving for variable 'x'. Combine like terms: 0 + 1000 = 1000 1000 + -160x + x2 = -1000 + 160x + -1x2 + 1000 + -160x + x2 Reorder the terms: 1000 + -160x + x2 = -1000 + 1000 + 160x + -160x + -1x2 + x2 Combine like terms: -1000 + 1000 = 0 1000 + -160x + x2 = 0 + 160x + -160x + -1x2 + x2 1000 + -160x + x2 = 160x + -160x + -1x2 + x2 Combine like terms: 160x + -160x = 0 1000 + -160x + x2 = 0 + -1x2 + x2 1000 + -160x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1000 + -160x + x2 = 0 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 = 153.484692283 x = 153.484692283 Simplifying x = 153.484692283Subproblem 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 = 6.515307717 x = 6.515307717 Simplifying x = 6.515307717Solution
The solution to the problem is based on the solutions from the subproblems. x = {153.484692283, 6.515307717}
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