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Simplifying x2 + -80x + 1600 = 39 Reorder the terms: 1600 + -80x + x2 = 39 Solving 1600 + -80x + x2 = 39 Solving for variable 'x'. Reorder the terms: 1600 + -39 + -80x + x2 = 39 + -39 Combine like terms: 1600 + -39 = 1561 1561 + -80x + x2 = 39 + -39 Combine like terms: 39 + -39 = 0 1561 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1561' to each side of the equation. 1561 + -80x + -1561 + x2 = 0 + -1561 Reorder the terms: 1561 + -1561 + -80x + x2 = 0 + -1561 Combine like terms: 1561 + -1561 = 0 0 + -80x + x2 = 0 + -1561 -80x + x2 = 0 + -1561 Combine like terms: 0 + -1561 = -1561 -80x + x2 = -1561 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -1561 + 1600 Reorder the terms: 1600 + -80x + x2 = -1561 + 1600 Combine like terms: -1561 + 1600 = 39 1600 + -80x + x2 = 39 Factor a perfect square on the left side: (x + -40)(x + -40) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -40) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -40 = 6.244997998 Simplifying x + -40 = 6.244997998 Reorder the terms: -40 + x = 6.244997998 Solving -40 + x = 6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 6.244997998 + 40 Combine like terms: -40 + 40 = 0 0 + x = 6.244997998 + 40 x = 6.244997998 + 40 Combine like terms: 6.244997998 + 40 = 46.244997998 x = 46.244997998 Simplifying x = 46.244997998Subproblem 2
x + -40 = -6.244997998 Simplifying x + -40 = -6.244997998 Reorder the terms: -40 + x = -6.244997998 Solving -40 + x = -6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -6.244997998 + 40 Combine like terms: -40 + 40 = 0 0 + x = -6.244997998 + 40 x = -6.244997998 + 40 Combine like terms: -6.244997998 + 40 = 33.755002002 x = 33.755002002 Simplifying x = 33.755002002Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.244997998, 33.755002002}
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