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Simplifying 500 = 0.08x + 0.004x2 Solving 500 = 0.08x + 0.004x2 Solving for variable 'x'. Reorder the terms: 500 + -0.08x + -0.004x2 = 0.08x + -0.08x + 0.004x2 + -0.004x2 Combine like terms: 0.08x + -0.08x = 0.00 500 + -0.08x + -0.004x2 = 0.00 + 0.004x2 + -0.004x2 500 + -0.08x + -0.004x2 = 0.004x2 + -0.004x2 Combine like terms: 0.004x2 + -0.004x2 = 0.000 500 + -0.08x + -0.004x2 = 0.000 Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. -125000 + 20x + x2 = 0 Move the constant term to the right: Add '125000' to each side of the equation. -125000 + 20x + 125000 + x2 = 0 + 125000 Reorder the terms: -125000 + 125000 + 20x + x2 = 0 + 125000 Combine like terms: -125000 + 125000 = 0 0 + 20x + x2 = 0 + 125000 20x + x2 = 0 + 125000 Combine like terms: 0 + 125000 = 125000 20x + x2 = 125000 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 = 125000 + 100 Reorder the terms: 100 + 20x + x2 = 125000 + 100 Combine like terms: 125000 + 100 = 125100 100 + 20x + x2 = 125100 Factor a perfect square on the left side: (x + 10)(x + 10) = 125100 Calculate the square root of the right side: 353.694783677 Break this problem into two subproblems by setting (x + 10) equal to 353.694783677 and -353.694783677.Subproblem 1
x + 10 = 353.694783677 Simplifying x + 10 = 353.694783677 Reorder the terms: 10 + x = 353.694783677 Solving 10 + x = 353.694783677 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 = 353.694783677 + -10 Combine like terms: 10 + -10 = 0 0 + x = 353.694783677 + -10 x = 353.694783677 + -10 Combine like terms: 353.694783677 + -10 = 343.694783677 x = 343.694783677 Simplifying x = 343.694783677Subproblem 2
x + 10 = -353.694783677 Simplifying x + 10 = -353.694783677 Reorder the terms: 10 + x = -353.694783677 Solving 10 + x = -353.694783677 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 = -353.694783677 + -10 Combine like terms: 10 + -10 = 0 0 + x = -353.694783677 + -10 x = -353.694783677 + -10 Combine like terms: -353.694783677 + -10 = -363.694783677 x = -363.694783677 Simplifying x = -363.694783677Solution
The solution to the problem is based on the solutions from the subproblems. x = {343.694783677, -363.694783677}
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