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Simplifying x2 + -20x = -9 Reorder the terms: -20x + x2 = -9 Solving -20x + x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + -20x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -20x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -20x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -20x + x2 = 0 + -9 -20x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -20x + x2 = -9 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 = -9 + 100 Reorder the terms: 100 + -20x + x2 = -9 + 100 Combine like terms: -9 + 100 = 91 100 + -20x + x2 = 91 Factor a perfect square on the left side: (x + -10)(x + -10) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -10) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -10 = 9.539392014 Simplifying x + -10 = 9.539392014 Reorder the terms: -10 + x = 9.539392014 Solving -10 + x = 9.539392014 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 = 9.539392014 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.539392014 + 10 x = 9.539392014 + 10 Combine like terms: 9.539392014 + 10 = 19.539392014 x = 19.539392014 Simplifying x = 19.539392014Subproblem 2
x + -10 = -9.539392014 Simplifying x + -10 = -9.539392014 Reorder the terms: -10 + x = -9.539392014 Solving -10 + x = -9.539392014 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 = -9.539392014 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.539392014 + 10 x = -9.539392014 + 10 Combine like terms: -9.539392014 + 10 = 0.460607986 x = 0.460607986 Simplifying x = 0.460607986Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.539392014, 0.460607986}
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