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Simplifying 0.03x + 0.0001x2 = 2.2 Solving 0.03x + 0.0001x2 = 2.2 Solving for variable 'x'. Reorder the terms: -2.2 + 0.03x + 0.0001x2 = 2.2 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 -2.2 + 0.03x + 0.0001x2 = 0.0 Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -22000 + 300x + x2 = 0 Move the constant term to the right: Add '22000' to each side of the equation. -22000 + 300x + 22000 + x2 = 0 + 22000 Reorder the terms: -22000 + 22000 + 300x + x2 = 0 + 22000 Combine like terms: -22000 + 22000 = 0 0 + 300x + x2 = 0 + 22000 300x + x2 = 0 + 22000 Combine like terms: 0 + 22000 = 22000 300x + x2 = 22000 The x term is 300x. Take half its coefficient (150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. 300x + 22500 + x2 = 22000 + 22500 Reorder the terms: 22500 + 300x + x2 = 22000 + 22500 Combine like terms: 22000 + 22500 = 44500 22500 + 300x + x2 = 44500 Factor a perfect square on the left side: (x + 150)(x + 150) = 44500 Calculate the square root of the right side: 210.950231097 Break this problem into two subproblems by setting (x + 150) equal to 210.950231097 and -210.950231097.Subproblem 1
x + 150 = 210.950231097 Simplifying x + 150 = 210.950231097 Reorder the terms: 150 + x = 210.950231097 Solving 150 + x = 210.950231097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = 210.950231097 + -150 Combine like terms: 150 + -150 = 0 0 + x = 210.950231097 + -150 x = 210.950231097 + -150 Combine like terms: 210.950231097 + -150 = 60.950231097 x = 60.950231097 Simplifying x = 60.950231097Subproblem 2
x + 150 = -210.950231097 Simplifying x + 150 = -210.950231097 Reorder the terms: 150 + x = -210.950231097 Solving 150 + x = -210.950231097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = -210.950231097 + -150 Combine like terms: 150 + -150 = 0 0 + x = -210.950231097 + -150 x = -210.950231097 + -150 Combine like terms: -210.950231097 + -150 = -360.950231097 x = -360.950231097 Simplifying x = -360.950231097Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.950231097, -360.950231097}
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