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Simplifying 0 = 400x + -5x2 + -5 Reorder the terms: 0 = -5 + 400x + -5x2 Solving 0 = -5 + 400x + -5x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -400x + 5x2 = -5 + 400x + -5x2 + 5 + -400x + 5x2 Reorder the terms: 5 + -400x + 5x2 = -5 + 5 + 400x + -400x + -5x2 + 5x2 Combine like terms: -5 + 5 = 0 5 + -400x + 5x2 = 0 + 400x + -400x + -5x2 + 5x2 5 + -400x + 5x2 = 400x + -400x + -5x2 + 5x2 Combine like terms: 400x + -400x = 0 5 + -400x + 5x2 = 0 + -5x2 + 5x2 5 + -400x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 5 + -400x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -80x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -80x + x2)' equal to zero and attempt to solve: Simplifying 1 + -80x + x2 = 0 Solving 1 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -80x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -80x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -80x + x2 = 0 + -1 -80x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -80x + x2 = -1 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -1 + 1600 Reorder the terms: 1600 + -80x + x2 = -1 + 1600 Combine like terms: -1 + 1600 = 1599 1600 + -80x + x2 = 1599 Factor a perfect square on the left side: (x + -40)(x + -40) = 1599 Calculate the square root of the right side: 39.987498046 Break this problem into two subproblems by setting (x + -40) equal to 39.987498046 and -39.987498046.Subproblem 1
x + -40 = 39.987498046 Simplifying x + -40 = 39.987498046 Reorder the terms: -40 + x = 39.987498046 Solving -40 + x = 39.987498046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 39.987498046 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.987498046 + 40 x = 39.987498046 + 40 Combine like terms: 39.987498046 + 40 = 79.987498046 x = 79.987498046 Simplifying x = 79.987498046Subproblem 2
x + -40 = -39.987498046 Simplifying x + -40 = -39.987498046 Reorder the terms: -40 + x = -39.987498046 Solving -40 + x = -39.987498046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -39.987498046 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.987498046 + 40 x = -39.987498046 + 40 Combine like terms: -39.987498046 + 40 = 0.012501954 x = 0.012501954 Simplifying x = 0.012501954Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.987498046, 0.012501954}Solution
x = {79.987498046, 0.012501954}
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