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Simplifying x2 + 20x + 11 = 0 Reorder the terms: 11 + 20x + x2 = 0 Solving 11 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 20x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 20x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 20x + x2 = 0 + -11 20x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 20x + x2 = -11 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 = -11 + 100 Reorder the terms: 100 + 20x + x2 = -11 + 100 Combine like terms: -11 + 100 = 89 100 + 20x + x2 = 89 Factor a perfect square on the left side: (x + 10)(x + 10) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 10) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 10 = 9.433981132 Simplifying x + 10 = 9.433981132 Reorder the terms: 10 + x = 9.433981132 Solving 10 + x = 9.433981132 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 = 9.433981132 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.433981132 + -10 x = 9.433981132 + -10 Combine like terms: 9.433981132 + -10 = -0.566018868 x = -0.566018868 Simplifying x = -0.566018868Subproblem 2
x + 10 = -9.433981132 Simplifying x + 10 = -9.433981132 Reorder the terms: 10 + x = -9.433981132 Solving 10 + x = -9.433981132 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 = -9.433981132 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.433981132 + -10 x = -9.433981132 + -10 Combine like terms: -9.433981132 + -10 = -19.433981132 x = -19.433981132 Simplifying x = -19.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.566018868, -19.433981132}
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