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Simplifying 0 = -0.005x2 + 2x + 5 Reorder the terms: 0 = 5 + 2x + -0.005x2 Solving 0 = 5 + 2x + -0.005x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -2x + 0.005x2 = 5 + 2x + -0.005x2 + -5 + -2x + 0.005x2 Reorder the terms: -5 + -2x + 0.005x2 = 5 + -5 + 2x + -2x + -0.005x2 + 0.005x2 Combine like terms: 5 + -5 = 0 -5 + -2x + 0.005x2 = 0 + 2x + -2x + -0.005x2 + 0.005x2 -5 + -2x + 0.005x2 = 2x + -2x + -0.005x2 + 0.005x2 Combine like terms: 2x + -2x = 0 -5 + -2x + 0.005x2 = 0 + -0.005x2 + 0.005x2 -5 + -2x + 0.005x2 = -0.005x2 + 0.005x2 Combine like terms: -0.005x2 + 0.005x2 = 0.000 -5 + -2x + 0.005x2 = 0.000 Begin completing the square. Divide all terms by 0.005 the coefficient of the squared term: Divide each side by '0.005'. -1000 + -400x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -400x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -400x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -400x + x2 = 0 + 1000 -400x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -400x + x2 = 1000 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = 1000 + 40000 Reorder the terms: 40000 + -400x + x2 = 1000 + 40000 Combine like terms: 1000 + 40000 = 41000 40000 + -400x + x2 = 41000 Factor a perfect square on the left side: (x + -200)(x + -200) = 41000 Calculate the square root of the right side: 202.484567313 Break this problem into two subproblems by setting (x + -200) equal to 202.484567313 and -202.484567313.Subproblem 1
x + -200 = 202.484567313 Simplifying x + -200 = 202.484567313 Reorder the terms: -200 + x = 202.484567313 Solving -200 + x = 202.484567313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 202.484567313 + 200 Combine like terms: -200 + 200 = 0 0 + x = 202.484567313 + 200 x = 202.484567313 + 200 Combine like terms: 202.484567313 + 200 = 402.484567313 x = 402.484567313 Simplifying x = 402.484567313Subproblem 2
x + -200 = -202.484567313 Simplifying x + -200 = -202.484567313 Reorder the terms: -200 + x = -202.484567313 Solving -200 + x = -202.484567313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -202.484567313 + 200 Combine like terms: -200 + 200 = 0 0 + x = -202.484567313 + 200 x = -202.484567313 + 200 Combine like terms: -202.484567313 + 200 = -2.484567313 x = -2.484567313 Simplifying x = -2.484567313Solution
The solution to the problem is based on the solutions from the subproblems. x = {402.484567313, -2.484567313}
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