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Simplifying 160x + (x * x) = 4500 Multiply x * x 160x + (x2) = 4500 160x + x2 = 4500 Solving 160x + x2 = 4500 Solving for variable 'x'. Reorder the terms: -4500 + 160x + x2 = 4500 + -4500 Combine like terms: 4500 + -4500 = 0 -4500 + 160x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4500' to each side of the equation. -4500 + 160x + 4500 + x2 = 0 + 4500 Reorder the terms: -4500 + 4500 + 160x + x2 = 0 + 4500 Combine like terms: -4500 + 4500 = 0 0 + 160x + x2 = 0 + 4500 160x + x2 = 0 + 4500 Combine like terms: 0 + 4500 = 4500 160x + x2 = 4500 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 = 4500 + 6400 Reorder the terms: 6400 + 160x + x2 = 4500 + 6400 Combine like terms: 4500 + 6400 = 10900 6400 + 160x + x2 = 10900 Factor a perfect square on the left side: (x + 80)(x + 80) = 10900 Calculate the square root of the right side: 104.403065089 Break this problem into two subproblems by setting (x + 80) equal to 104.403065089 and -104.403065089.Subproblem 1
x + 80 = 104.403065089 Simplifying x + 80 = 104.403065089 Reorder the terms: 80 + x = 104.403065089 Solving 80 + x = 104.403065089 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 = 104.403065089 + -80 Combine like terms: 80 + -80 = 0 0 + x = 104.403065089 + -80 x = 104.403065089 + -80 Combine like terms: 104.403065089 + -80 = 24.403065089 x = 24.403065089 Simplifying x = 24.403065089Subproblem 2
x + 80 = -104.403065089 Simplifying x + 80 = -104.403065089 Reorder the terms: 80 + x = -104.403065089 Solving 80 + x = -104.403065089 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 = -104.403065089 + -80 Combine like terms: 80 + -80 = 0 0 + x = -104.403065089 + -80 x = -104.403065089 + -80 Combine like terms: -104.403065089 + -80 = -184.403065089 x = -184.403065089 Simplifying x = -184.403065089Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.403065089, -184.403065089}
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