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Simplifying x2 + 20x + 18 = 100 Reorder the terms: 18 + 20x + x2 = 100 Solving 18 + 20x + x2 = 100 Solving for variable 'x'. Reorder the terms: 18 + -100 + 20x + x2 = 100 + -100 Combine like terms: 18 + -100 = -82 -82 + 20x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -82 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + 20x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + 20x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 20x + x2 = 0 + 82 20x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 20x + x2 = 82 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 = 82 + 100 Reorder the terms: 100 + 20x + x2 = 82 + 100 Combine like terms: 82 + 100 = 182 100 + 20x + x2 = 182 Factor a perfect square on the left side: (x + 10)(x + 10) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (x + 10) equal to 13.490737563 and -13.490737563.Subproblem 1
x + 10 = 13.490737563 Simplifying x + 10 = 13.490737563 Reorder the terms: 10 + x = 13.490737563 Solving 10 + x = 13.490737563 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 = 13.490737563 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.490737563 + -10 x = 13.490737563 + -10 Combine like terms: 13.490737563 + -10 = 3.490737563 x = 3.490737563 Simplifying x = 3.490737563Subproblem 2
x + 10 = -13.490737563 Simplifying x + 10 = -13.490737563 Reorder the terms: 10 + x = -13.490737563 Solving 10 + x = -13.490737563 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 = -13.490737563 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.490737563 + -10 x = -13.490737563 + -10 Combine like terms: -13.490737563 + -10 = -23.490737563 x = -23.490737563 Simplifying x = -23.490737563Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.490737563, -23.490737563}
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