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Simplifying -0.5 = -0.025x2 + x Reorder the terms: -0.5 = x + -0.025x2 Solving -0.5 = x + -0.025x2 Solving for variable 'x'. Reorder the terms: -0.5 + -1x + 0.025x2 = x + -1x + -0.025x2 + 0.025x2 Combine like terms: x + -1x = 0 -0.5 + -1x + 0.025x2 = 0 + -0.025x2 + 0.025x2 -0.5 + -1x + 0.025x2 = -0.025x2 + 0.025x2 Combine like terms: -0.025x2 + 0.025x2 = 0.000 -0.5 + -1x + 0.025x2 = 0.000 Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. -20 + -40x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -40x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -40x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -40x + x2 = 0 + 20 -40x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -40x + x2 = 20 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 20 + 400 Reorder the terms: 400 + -40x + x2 = 20 + 400 Combine like terms: 20 + 400 = 420 400 + -40x + x2 = 420 Factor a perfect square on the left side: (x + -20)(x + -20) = 420 Calculate the square root of the right side: 20.493901532 Break this problem into two subproblems by setting (x + -20) equal to 20.493901532 and -20.493901532.Subproblem 1
x + -20 = 20.493901532 Simplifying x + -20 = 20.493901532 Reorder the terms: -20 + x = 20.493901532 Solving -20 + x = 20.493901532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 20.493901532 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.493901532 + 20 x = 20.493901532 + 20 Combine like terms: 20.493901532 + 20 = 40.493901532 x = 40.493901532 Simplifying x = 40.493901532Subproblem 2
x + -20 = -20.493901532 Simplifying x + -20 = -20.493901532 Reorder the terms: -20 + x = -20.493901532 Solving -20 + x = -20.493901532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -20.493901532 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.493901532 + 20 x = -20.493901532 + 20 Combine like terms: -20.493901532 + 20 = -0.493901532 x = -0.493901532 Simplifying x = -0.493901532Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.493901532, -0.493901532}
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