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Simplifying x2 + 20x = 20 Reorder the terms: 20x + x2 = 20 Solving 20x + x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 20x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 20x + x2 = 0 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 = 0.95445115 x = 0.95445115 Simplifying x = 0.95445115Subproblem 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 = -20.95445115 x = -20.95445115 Simplifying x = -20.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.95445115, -20.95445115}
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