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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 = 10.25 30.25 + -11x + x2 = 10.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -5.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -5.5 = 3.201562119 Simplifying x + -5.5 = 3.201562119 Reorder the terms: -5.5 + x = 3.201562119 Solving -5.5 + x = 3.201562119 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 = 3.201562119 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 3.201562119 + 5.5 x = 3.201562119 + 5.5 Combine like terms: 3.201562119 + 5.5 = 8.701562119 x = 8.701562119 Simplifying x = 8.701562119Subproblem 2
x + -5.5 = -3.201562119 Simplifying x + -5.5 = -3.201562119 Reorder the terms: -5.5 + x = -3.201562119 Solving -5.5 + x = -3.201562119 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 = -3.201562119 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -3.201562119 + 5.5 x = -3.201562119 + 5.5 Combine like terms: -3.201562119 + 5.5 = 2.298437881 x = 2.298437881 Simplifying x = 2.298437881Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.701562119, 2.298437881}
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