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Simplifying 5000 = -5x2 + 400x + 5 Reorder the terms: 5000 = 5 + 400x + -5x2 Solving 5000 = 5 + 400x + -5x2 Solving for variable 'x'. Combine like terms: 5000 + -5 = 4995 4995 + -400x + 5x2 = 5 + 400x + -5x2 + -5 + -400x + 5x2 Reorder the terms: 4995 + -400x + 5x2 = 5 + -5 + 400x + -400x + -5x2 + 5x2 Combine like terms: 5 + -5 = 0 4995 + -400x + 5x2 = 0 + 400x + -400x + -5x2 + 5x2 4995 + -400x + 5x2 = 400x + -400x + -5x2 + 5x2 Combine like terms: 400x + -400x = 0 4995 + -400x + 5x2 = 0 + -5x2 + 5x2 4995 + -400x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 4995 + -400x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(999 + -80x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(999 + -80x + x2)' equal to zero and attempt to solve: Simplifying 999 + -80x + x2 = 0 Solving 999 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-999' to each side of the equation. 999 + -80x + -999 + x2 = 0 + -999 Reorder the terms: 999 + -999 + -80x + x2 = 0 + -999 Combine like terms: 999 + -999 = 0 0 + -80x + x2 = 0 + -999 -80x + x2 = 0 + -999 Combine like terms: 0 + -999 = -999 -80x + x2 = -999 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 = -999 + 1600 Reorder the terms: 1600 + -80x + x2 = -999 + 1600 Combine like terms: -999 + 1600 = 601 1600 + -80x + x2 = 601 Factor a perfect square on the left side: (x + -40)(x + -40) = 601 Calculate the square root of the right side: 24.515301344 Break this problem into two subproblems by setting (x + -40) equal to 24.515301344 and -24.515301344.Subproblem 1
x + -40 = 24.515301344 Simplifying x + -40 = 24.515301344 Reorder the terms: -40 + x = 24.515301344 Solving -40 + x = 24.515301344 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 = 24.515301344 + 40 Combine like terms: -40 + 40 = 0 0 + x = 24.515301344 + 40 x = 24.515301344 + 40 Combine like terms: 24.515301344 + 40 = 64.515301344 x = 64.515301344 Simplifying x = 64.515301344Subproblem 2
x + -40 = -24.515301344 Simplifying x + -40 = -24.515301344 Reorder the terms: -40 + x = -24.515301344 Solving -40 + x = -24.515301344 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 = -24.515301344 + 40 Combine like terms: -40 + 40 = 0 0 + x = -24.515301344 + 40 x = -24.515301344 + 40 Combine like terms: -24.515301344 + 40 = 15.484698656 x = 15.484698656 Simplifying x = 15.484698656Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.515301344, 15.484698656}Solution
x = {64.515301344, 15.484698656}
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