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Simplifying x2 + 11x + -20 = 0 Reorder the terms: -20 + 11x + x2 = 0 Solving -20 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 11x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 11x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 11x + x2 = 0 + 20 11x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 11x + x2 = 20 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 20 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 20 + 30.25 Combine like terms: 20 + 30.25 = 50.25 30.25 + 11x + x2 = 50.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + 5.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + 5.5 = 7.088723439 Simplifying x + 5.5 = 7.088723439 Reorder the terms: 5.5 + x = 7.088723439 Solving 5.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.088723439 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.088723439 + -5.5 x = 7.088723439 + -5.5 Combine like terms: 7.088723439 + -5.5 = 1.588723439 x = 1.588723439 Simplifying x = 1.588723439Subproblem 2
x + 5.5 = -7.088723439 Simplifying x + 5.5 = -7.088723439 Reorder the terms: 5.5 + x = -7.088723439 Solving 5.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.088723439 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.088723439 + -5.5 x = -7.088723439 + -5.5 Combine like terms: -7.088723439 + -5.5 = -12.588723439 x = -12.588723439 Simplifying x = -12.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.588723439, -12.588723439}
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