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Simplifying x2 + -20x = 39 Reorder the terms: -20x + x2 = 39 Solving -20x + x2 = 39 Solving for variable 'x'. Reorder the terms: -39 + -20x + x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -20x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -20x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -20x + x2 = 0 + 39 -20x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -20x + x2 = 39 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 = 39 + 100 Reorder the terms: 100 + -20x + x2 = 39 + 100 Combine like terms: 39 + 100 = 139 100 + -20x + x2 = 139 Factor a perfect square on the left side: (x + -10)(x + -10) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (x + -10) equal to 11.789826123 and -11.789826123.Subproblem 1
x + -10 = 11.789826123 Simplifying x + -10 = 11.789826123 Reorder the terms: -10 + x = 11.789826123 Solving -10 + x = 11.789826123 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 = 11.789826123 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.789826123 + 10 x = 11.789826123 + 10 Combine like terms: 11.789826123 + 10 = 21.789826123 x = 21.789826123 Simplifying x = 21.789826123Subproblem 2
x + -10 = -11.789826123 Simplifying x + -10 = -11.789826123 Reorder the terms: -10 + x = -11.789826123 Solving -10 + x = -11.789826123 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 = -11.789826123 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.789826123 + 10 x = -11.789826123 + 10 Combine like terms: -11.789826123 + 10 = -1.789826123 x = -1.789826123 Simplifying x = -1.789826123Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.789826123, -1.789826123}
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