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Simplifying x2 + 20x + -9909 = 0 Reorder the terms: -9909 + 20x + x2 = 0 Solving -9909 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9909' to each side of the equation. -9909 + 20x + 9909 + x2 = 0 + 9909 Reorder the terms: -9909 + 9909 + 20x + x2 = 0 + 9909 Combine like terms: -9909 + 9909 = 0 0 + 20x + x2 = 0 + 9909 20x + x2 = 0 + 9909 Combine like terms: 0 + 9909 = 9909 20x + x2 = 9909 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 = 9909 + 100 Reorder the terms: 100 + 20x + x2 = 9909 + 100 Combine like terms: 9909 + 100 = 10009 100 + 20x + x2 = 10009 Factor a perfect square on the left side: (x + 10)(x + 10) = 10009 Calculate the square root of the right side: 100.04498988 Break this problem into two subproblems by setting (x + 10) equal to 100.04498988 and -100.04498988.Subproblem 1
x + 10 = 100.04498988 Simplifying x + 10 = 100.04498988 Reorder the terms: 10 + x = 100.04498988 Solving 10 + x = 100.04498988 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 = 100.04498988 + -10 Combine like terms: 10 + -10 = 0 0 + x = 100.04498988 + -10 x = 100.04498988 + -10 Combine like terms: 100.04498988 + -10 = 90.04498988 x = 90.04498988 Simplifying x = 90.04498988Subproblem 2
x + 10 = -100.04498988 Simplifying x + 10 = -100.04498988 Reorder the terms: 10 + x = -100.04498988 Solving 10 + x = -100.04498988 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 = -100.04498988 + -10 Combine like terms: 10 + -10 = 0 0 + x = -100.04498988 + -10 x = -100.04498988 + -10 Combine like terms: -100.04498988 + -10 = -110.04498988 x = -110.04498988 Simplifying x = -110.04498988Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.04498988, -110.04498988}
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