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Simplifying x2 + -20x + 82 = 0 Reorder the terms: 82 + -20x + x2 = 0 Solving 82 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-82' to each side of the equation. 82 + -20x + -82 + x2 = 0 + -82 Reorder the terms: 82 + -82 + -20x + x2 = 0 + -82 Combine like terms: 82 + -82 = 0 0 + -20x + x2 = 0 + -82 -20x + x2 = 0 + -82 Combine like terms: 0 + -82 = -82 -20x + x2 = -82 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -82 + 100 Reorder the terms: 100 + -20x + x2 = -82 + 100 Combine like terms: -82 + 100 = 18 100 + -20x + x2 = 18 Factor a perfect square on the left side: (x + -10)(x + -10) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -10) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -10 = 4.242640687 Simplifying x + -10 = 4.242640687 Reorder the terms: -10 + x = 4.242640687 Solving -10 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 4.242640687 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4.242640687 + 10 x = 4.242640687 + 10 Combine like terms: 4.242640687 + 10 = 14.242640687 x = 14.242640687 Simplifying x = 14.242640687Subproblem 2
x + -10 = -4.242640687 Simplifying x + -10 = -4.242640687 Reorder the terms: -10 + x = -4.242640687 Solving -10 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -4.242640687 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4.242640687 + 10 x = -4.242640687 + 10 Combine like terms: -4.242640687 + 10 = 5.757359313 x = 5.757359313 Simplifying x = 5.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.242640687, 5.757359313}
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