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Simplifying x2 + 20x + 100 = 39 Reorder the terms: 100 + 20x + x2 = 39 Solving 100 + 20x + x2 = 39 Solving for variable 'x'. Reorder the terms: 100 + -39 + 20x + x2 = 39 + -39 Combine like terms: 100 + -39 = 61 61 + 20x + x2 = 39 + -39 Combine like terms: 39 + -39 = 0 61 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-61' to each side of the equation. 61 + 20x + -61 + x2 = 0 + -61 Reorder the terms: 61 + -61 + 20x + x2 = 0 + -61 Combine like terms: 61 + -61 = 0 0 + 20x + x2 = 0 + -61 20x + x2 = 0 + -61 Combine like terms: 0 + -61 = -61 20x + x2 = -61 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 = -61 + 100 Reorder the terms: 100 + 20x + x2 = -61 + 100 Combine like terms: -61 + 100 = 39 100 + 20x + x2 = 39 Factor a perfect square on the left side: (x + 10)(x + 10) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 10) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 10 = 6.244997998 Simplifying x + 10 = 6.244997998 Reorder the terms: 10 + x = 6.244997998 Solving 10 + x = 6.244997998 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 = 6.244997998 + -10 Combine like terms: 10 + -10 = 0 0 + x = 6.244997998 + -10 x = 6.244997998 + -10 Combine like terms: 6.244997998 + -10 = -3.755002002 x = -3.755002002 Simplifying x = -3.755002002Subproblem 2
x + 10 = -6.244997998 Simplifying x + 10 = -6.244997998 Reorder the terms: 10 + x = -6.244997998 Solving 10 + x = -6.244997998 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 = -6.244997998 + -10 Combine like terms: 10 + -10 = 0 0 + x = -6.244997998 + -10 x = -6.244997998 + -10 Combine like terms: -6.244997998 + -10 = -16.244997998 x = -16.244997998 Simplifying x = -16.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.755002002, -16.244997998}
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