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Simplifying x * x + -82x + 60 = 0 Multiply x * x x2 + -82x + 60 = 0 Reorder the terms: 60 + -82x + x2 = 0 Solving 60 + -82x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -82x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -82x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -82x + x2 = 0 + -60 -82x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -82x + x2 = -60 The x term is -82x. Take half its coefficient (-41). Square it (1681) and add it to both sides. Add '1681' to each side of the equation. -82x + 1681 + x2 = -60 + 1681 Reorder the terms: 1681 + -82x + x2 = -60 + 1681 Combine like terms: -60 + 1681 = 1621 1681 + -82x + x2 = 1621 Factor a perfect square on the left side: (x + -41)(x + -41) = 1621 Calculate the square root of the right side: 40.261644278 Break this problem into two subproblems by setting (x + -41) equal to 40.261644278 and -40.261644278.Subproblem 1
x + -41 = 40.261644278 Simplifying x + -41 = 40.261644278 Reorder the terms: -41 + x = 40.261644278 Solving -41 + x = 40.261644278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = 40.261644278 + 41 Combine like terms: -41 + 41 = 0 0 + x = 40.261644278 + 41 x = 40.261644278 + 41 Combine like terms: 40.261644278 + 41 = 81.261644278 x = 81.261644278 Simplifying x = 81.261644278Subproblem 2
x + -41 = -40.261644278 Simplifying x + -41 = -40.261644278 Reorder the terms: -41 + x = -40.261644278 Solving -41 + x = -40.261644278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '41' to each side of the equation. -41 + 41 + x = -40.261644278 + 41 Combine like terms: -41 + 41 = 0 0 + x = -40.261644278 + 41 x = -40.261644278 + 41 Combine like terms: -40.261644278 + 41 = 0.738355722 x = 0.738355722 Simplifying x = 0.738355722Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.261644278, 0.738355722}
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