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Simplifying 20x + x2 = 39996 Solving 20x + x2 = 39996 Solving for variable 'x'. Reorder the terms: -39996 + 20x + x2 = 39996 + -39996 Combine like terms: 39996 + -39996 = 0 -39996 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39996' to each side of the equation. -39996 + 20x + 39996 + x2 = 0 + 39996 Reorder the terms: -39996 + 39996 + 20x + x2 = 0 + 39996 Combine like terms: -39996 + 39996 = 0 0 + 20x + x2 = 0 + 39996 20x + x2 = 0 + 39996 Combine like terms: 0 + 39996 = 39996 20x + x2 = 39996 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 = 39996 + 100 Reorder the terms: 100 + 20x + x2 = 39996 + 100 Combine like terms: 39996 + 100 = 40096 100 + 20x + x2 = 40096 Factor a perfect square on the left side: (x + 10)(x + 10) = 40096 Calculate the square root of the right side: 200.239856173 Break this problem into two subproblems by setting (x + 10) equal to 200.239856173 and -200.239856173.Subproblem 1
x + 10 = 200.239856173 Simplifying x + 10 = 200.239856173 Reorder the terms: 10 + x = 200.239856173 Solving 10 + x = 200.239856173 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 = 200.239856173 + -10 Combine like terms: 10 + -10 = 0 0 + x = 200.239856173 + -10 x = 200.239856173 + -10 Combine like terms: 200.239856173 + -10 = 190.239856173 x = 190.239856173 Simplifying x = 190.239856173Subproblem 2
x + 10 = -200.239856173 Simplifying x + 10 = -200.239856173 Reorder the terms: 10 + x = -200.239856173 Solving 10 + x = -200.239856173 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 = -200.239856173 + -10 Combine like terms: 10 + -10 = 0 0 + x = -200.239856173 + -10 x = -200.239856173 + -10 Combine like terms: -200.239856173 + -10 = -210.239856173 x = -210.239856173 Simplifying x = -210.239856173Solution
The solution to the problem is based on the solutions from the subproblems. x = {190.239856173, -210.239856173}
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