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Simplifying x2 + -20x + 23 = 0 Reorder the terms: 23 + -20x + x2 = 0 Solving 23 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -20x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -20x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -20x + x2 = 0 + -23 -20x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -20x + x2 = -23 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 = -23 + 100 Reorder the terms: 100 + -20x + x2 = -23 + 100 Combine like terms: -23 + 100 = 77 100 + -20x + x2 = 77 Factor a perfect square on the left side: (x + -10)(x + -10) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + -10) equal to 8.774964387 and -8.774964387.Subproblem 1
x + -10 = 8.774964387 Simplifying x + -10 = 8.774964387 Reorder the terms: -10 + x = 8.774964387 Solving -10 + x = 8.774964387 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 = 8.774964387 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.774964387 + 10 x = 8.774964387 + 10 Combine like terms: 8.774964387 + 10 = 18.774964387 x = 18.774964387 Simplifying x = 18.774964387Subproblem 2
x + -10 = -8.774964387 Simplifying x + -10 = -8.774964387 Reorder the terms: -10 + x = -8.774964387 Solving -10 + x = -8.774964387 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 = -8.774964387 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.774964387 + 10 x = -8.774964387 + 10 Combine like terms: -8.774964387 + 10 = 1.225035613 x = 1.225035613 Simplifying x = 1.225035613Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.774964387, 1.225035613}
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