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Simplifying x2 + 40x + -20 = 0 Reorder the terms: -20 + 40x + x2 = 0 Solving -20 + 40x + 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 + 40x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 40x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 40x + x2 = 0 + 20 40x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 40x + x2 = 20 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 20 + 400 Reorder the terms: 400 + 40x + x2 = 20 + 400 Combine like terms: 20 + 400 = 420 400 + 40x + x2 = 420 Factor a perfect square on the left side: (x + 20)(x + 20) = 420 Calculate the square root of the right side: 20.493901532 Break this problem into two subproblems by setting (x + 20) equal to 20.493901532 and -20.493901532.Subproblem 1
x + 20 = 20.493901532 Simplifying x + 20 = 20.493901532 Reorder the terms: 20 + x = 20.493901532 Solving 20 + x = 20.493901532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 20.493901532 + -20 Combine like terms: 20 + -20 = 0 0 + x = 20.493901532 + -20 x = 20.493901532 + -20 Combine like terms: 20.493901532 + -20 = 0.493901532 x = 0.493901532 Simplifying x = 0.493901532Subproblem 2
x + 20 = -20.493901532 Simplifying x + 20 = -20.493901532 Reorder the terms: 20 + x = -20.493901532 Solving 20 + x = -20.493901532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -20.493901532 + -20 Combine like terms: 20 + -20 = 0 0 + x = -20.493901532 + -20 x = -20.493901532 + -20 Combine like terms: -20.493901532 + -20 = -40.493901532 x = -40.493901532 Simplifying x = -40.493901532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.493901532, -40.493901532}
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