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Simplifying 10 = -0.01x2 + 4x Reorder the terms: 10 = 4x + -0.01x2 Solving 10 = 4x + -0.01x2 Solving for variable 'x'. Reorder the terms: 10 + -4x + 0.01x2 = 4x + -4x + -0.01x2 + 0.01x2 Combine like terms: 4x + -4x = 0 10 + -4x + 0.01x2 = 0 + -0.01x2 + 0.01x2 10 + -4x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 10 + -4x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 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 = 39000 40000 + -400x + x2 = 39000 Factor a perfect square on the left side: (x + -200)(x + -200) = 39000 Calculate the square root of the right side: 197.484176581 Break this problem into two subproblems by setting (x + -200) equal to 197.484176581 and -197.484176581.Subproblem 1
x + -200 = 197.484176581 Simplifying x + -200 = 197.484176581 Reorder the terms: -200 + x = 197.484176581 Solving -200 + x = 197.484176581 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 = 197.484176581 + 200 Combine like terms: -200 + 200 = 0 0 + x = 197.484176581 + 200 x = 197.484176581 + 200 Combine like terms: 197.484176581 + 200 = 397.484176581 x = 397.484176581 Simplifying x = 397.484176581Subproblem 2
x + -200 = -197.484176581 Simplifying x + -200 = -197.484176581 Reorder the terms: -200 + x = -197.484176581 Solving -200 + x = -197.484176581 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 = -197.484176581 + 200 Combine like terms: -200 + 200 = 0 0 + x = -197.484176581 + 200 x = -197.484176581 + 200 Combine like terms: -197.484176581 + 200 = 2.515823419 x = 2.515823419 Simplifying x = 2.515823419Solution
The solution to the problem is based on the solutions from the subproblems. x = {397.484176581, 2.515823419}
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