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Simplifying x2 + -89x + 160 = 0 Reorder the terms: 160 + -89x + x2 = 0 Solving 160 + -89x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-160' to each side of the equation. 160 + -89x + -160 + x2 = 0 + -160 Reorder the terms: 160 + -160 + -89x + x2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + -89x + x2 = 0 + -160 -89x + x2 = 0 + -160 Combine like terms: 0 + -160 = -160 -89x + x2 = -160 The x term is -89x. Take half its coefficient (-44.5). Square it (1980.25) and add it to both sides. Add '1980.25' to each side of the equation. -89x + 1980.25 + x2 = -160 + 1980.25 Reorder the terms: 1980.25 + -89x + x2 = -160 + 1980.25 Combine like terms: -160 + 1980.25 = 1820.25 1980.25 + -89x + x2 = 1820.25 Factor a perfect square on the left side: (x + -44.5)(x + -44.5) = 1820.25 Calculate the square root of the right side: 42.66438796 Break this problem into two subproblems by setting (x + -44.5) equal to 42.66438796 and -42.66438796.Subproblem 1
x + -44.5 = 42.66438796 Simplifying x + -44.5 = 42.66438796 Reorder the terms: -44.5 + x = 42.66438796 Solving -44.5 + x = 42.66438796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = 42.66438796 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = 42.66438796 + 44.5 x = 42.66438796 + 44.5 Combine like terms: 42.66438796 + 44.5 = 87.16438796 x = 87.16438796 Simplifying x = 87.16438796Subproblem 2
x + -44.5 = -42.66438796 Simplifying x + -44.5 = -42.66438796 Reorder the terms: -44.5 + x = -42.66438796 Solving -44.5 + x = -42.66438796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = -42.66438796 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = -42.66438796 + 44.5 x = -42.66438796 + 44.5 Combine like terms: -42.66438796 + 44.5 = 1.83561204 x = 1.83561204 Simplifying x = 1.83561204Solution
The solution to the problem is based on the solutions from the subproblems. x = {87.16438796, 1.83561204}
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