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Simplifying -1x * -1x + 160x + -6000 = 0 Reorder the terms for easier multiplication: -1 * -1x * x + 160x + -6000 = 0 Multiply -1 * -1 1x * x + 160x + -6000 = 0 Multiply x * x 1x2 + 160x + -6000 = 0 Reorder the terms: -6000 + 160x + 1x2 = 0 Solving -6000 + 160x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6000' to each side of the equation. -6000 + 160x + 6000 + x2 = 0 + 6000 Reorder the terms: -6000 + 6000 + 160x + x2 = 0 + 6000 Combine like terms: -6000 + 6000 = 0 0 + 160x + x2 = 0 + 6000 160x + x2 = 0 + 6000 Combine like terms: 0 + 6000 = 6000 160x + x2 = 6000 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 = 6000 + 6400 Reorder the terms: 6400 + 160x + x2 = 6000 + 6400 Combine like terms: 6000 + 6400 = 12400 6400 + 160x + x2 = 12400 Factor a perfect square on the left side: (x + 80)(x + 80) = 12400 Calculate the square root of the right side: 111.355287257 Break this problem into two subproblems by setting (x + 80) equal to 111.355287257 and -111.355287257.Subproblem 1
x + 80 = 111.355287257 Simplifying x + 80 = 111.355287257 Reorder the terms: 80 + x = 111.355287257 Solving 80 + x = 111.355287257 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 = 111.355287257 + -80 Combine like terms: 80 + -80 = 0 0 + x = 111.355287257 + -80 x = 111.355287257 + -80 Combine like terms: 111.355287257 + -80 = 31.355287257 x = 31.355287257 Simplifying x = 31.355287257Subproblem 2
x + 80 = -111.355287257 Simplifying x + 80 = -111.355287257 Reorder the terms: 80 + x = -111.355287257 Solving 80 + x = -111.355287257 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 = -111.355287257 + -80 Combine like terms: 80 + -80 = 0 0 + x = -111.355287257 + -80 x = -111.355287257 + -80 Combine like terms: -111.355287257 + -80 = -191.355287257 x = -191.355287257 Simplifying x = -191.355287257Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.355287257, -191.355287257}
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