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Simplifying x2 + -20x + -20 = 0 Reorder the terms: -20 + -20x + x2 = 0 Solving -20 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -20x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -20x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -20x + x2 = 0 + 20 -20x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -20x + x2 = 20 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 = 20 + 100 Reorder the terms: 100 + -20x + x2 = 20 + 100 Combine like terms: 20 + 100 = 120 100 + -20x + x2 = 120 Factor a perfect square on the left side: (x + -10)(x + -10) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + -10) equal to 10.95445115 and -10.95445115.Subproblem 1
x + -10 = 10.95445115 Simplifying x + -10 = 10.95445115 Reorder the terms: -10 + x = 10.95445115 Solving -10 + x = 10.95445115 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 = 10.95445115 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.95445115 + 10 x = 10.95445115 + 10 Combine like terms: 10.95445115 + 10 = 20.95445115 x = 20.95445115 Simplifying x = 20.95445115Subproblem 2
x + -10 = -10.95445115 Simplifying x + -10 = -10.95445115 Reorder the terms: -10 + x = -10.95445115 Solving -10 + x = -10.95445115 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 = -10.95445115 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.95445115 + 10 x = -10.95445115 + 10 Combine like terms: -10.95445115 + 10 = -0.95445115 x = -0.95445115 Simplifying x = -0.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.95445115, -0.95445115}
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