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Simplifying x2 + 44x + 64 = 0 Reorder the terms: 64 + 44x + x2 = 0 Solving 64 + 44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 44x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 44x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 44x + x2 = 0 + -64 44x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 44x + x2 = -64 The x term is 44x. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x + 484 + x2 = -64 + 484 Reorder the terms: 484 + 44x + x2 = -64 + 484 Combine like terms: -64 + 484 = 420 484 + 44x + x2 = 420 Factor a perfect square on the left side: (x + 22)(x + 22) = 420 Calculate the square root of the right side: 20.493901532 Break this problem into two subproblems by setting (x + 22) equal to 20.493901532 and -20.493901532.Subproblem 1
x + 22 = 20.493901532 Simplifying x + 22 = 20.493901532 Reorder the terms: 22 + x = 20.493901532 Solving 22 + x = 20.493901532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 20.493901532 + -22 Combine like terms: 22 + -22 = 0 0 + x = 20.493901532 + -22 x = 20.493901532 + -22 Combine like terms: 20.493901532 + -22 = -1.506098468 x = -1.506098468 Simplifying x = -1.506098468Subproblem 2
x + 22 = -20.493901532 Simplifying x + 22 = -20.493901532 Reorder the terms: 22 + x = -20.493901532 Solving 22 + x = -20.493901532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = -20.493901532 + -22 Combine like terms: 22 + -22 = 0 0 + x = -20.493901532 + -22 x = -20.493901532 + -22 Combine like terms: -20.493901532 + -22 = -42.493901532 x = -42.493901532 Simplifying x = -42.493901532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.506098468, -42.493901532}
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