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Simplifying x * x + -80x + 75 = 0 Multiply x * x x2 + -80x + 75 = 0 Reorder the terms: 75 + -80x + x2 = 0 Solving 75 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -80x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -80x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -80x + x2 = 0 + -75 -80x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -80x + x2 = -75 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 = -75 + 1600 Reorder the terms: 1600 + -80x + x2 = -75 + 1600 Combine like terms: -75 + 1600 = 1525 1600 + -80x + x2 = 1525 Factor a perfect square on the left side: (x + -40)(x + -40) = 1525 Calculate the square root of the right side: 39.05124838 Break this problem into two subproblems by setting (x + -40) equal to 39.05124838 and -39.05124838.Subproblem 1
x + -40 = 39.05124838 Simplifying x + -40 = 39.05124838 Reorder the terms: -40 + x = 39.05124838 Solving -40 + x = 39.05124838 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 = 39.05124838 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.05124838 + 40 x = 39.05124838 + 40 Combine like terms: 39.05124838 + 40 = 79.05124838 x = 79.05124838 Simplifying x = 79.05124838Subproblem 2
x + -40 = -39.05124838 Simplifying x + -40 = -39.05124838 Reorder the terms: -40 + x = -39.05124838 Solving -40 + x = -39.05124838 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 = -39.05124838 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.05124838 + 40 x = -39.05124838 + 40 Combine like terms: -39.05124838 + 40 = 0.94875162 x = 0.94875162 Simplifying x = 0.94875162Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.05124838, 0.94875162}
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