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Simplifying x2 + 20x + 97 = 0 Reorder the terms: 97 + 20x + x2 = 0 Solving 97 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-97' to each side of the equation. 97 + 20x + -97 + x2 = 0 + -97 Reorder the terms: 97 + -97 + 20x + x2 = 0 + -97 Combine like terms: 97 + -97 = 0 0 + 20x + x2 = 0 + -97 20x + x2 = 0 + -97 Combine like terms: 0 + -97 = -97 20x + x2 = -97 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 = -97 + 100 Reorder the terms: 100 + 20x + x2 = -97 + 100 Combine like terms: -97 + 100 = 3 100 + 20x + x2 = 3 Factor a perfect square on the left side: (x + 10)(x + 10) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 10) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 10 = 1.732050808 Simplifying x + 10 = 1.732050808 Reorder the terms: 10 + x = 1.732050808 Solving 10 + x = 1.732050808 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 = 1.732050808 + -10 Combine like terms: 10 + -10 = 0 0 + x = 1.732050808 + -10 x = 1.732050808 + -10 Combine like terms: 1.732050808 + -10 = -8.267949192 x = -8.267949192 Simplifying x = -8.267949192Subproblem 2
x + 10 = -1.732050808 Simplifying x + 10 = -1.732050808 Reorder the terms: 10 + x = -1.732050808 Solving 10 + x = -1.732050808 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 = -1.732050808 + -10 Combine like terms: 10 + -10 = 0 0 + x = -1.732050808 + -10 x = -1.732050808 + -10 Combine like terms: -1.732050808 + -10 = -11.732050808 x = -11.732050808 Simplifying x = -11.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.267949192, -11.732050808}
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