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Simplifying 0.25x2 + 20x + 100 = 0 Reorder the terms: 100 + 20x + 0.25x2 = 0 Solving 100 + 20x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 400 + 80x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + 80x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + 80x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + 80x + x2 = 0 + -400 80x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 80x + x2 = -400 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = -400 + 1600 Reorder the terms: 1600 + 80x + x2 = -400 + 1600 Combine like terms: -400 + 1600 = 1200 1600 + 80x + x2 = 1200 Factor a perfect square on the left side: (x + 40)(x + 40) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (x + 40) equal to 34.641016151 and -34.641016151.Subproblem 1
x + 40 = 34.641016151 Simplifying x + 40 = 34.641016151 Reorder the terms: 40 + x = 34.641016151 Solving 40 + x = 34.641016151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 34.641016151 + -40 Combine like terms: 40 + -40 = 0 0 + x = 34.641016151 + -40 x = 34.641016151 + -40 Combine like terms: 34.641016151 + -40 = -5.358983849 x = -5.358983849 Simplifying x = -5.358983849Subproblem 2
x + 40 = -34.641016151 Simplifying x + 40 = -34.641016151 Reorder the terms: 40 + x = -34.641016151 Solving 40 + x = -34.641016151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -34.641016151 + -40 Combine like terms: 40 + -40 = 0 0 + x = -34.641016151 + -40 x = -34.641016151 + -40 Combine like terms: -34.641016151 + -40 = -74.641016151 x = -74.641016151 Simplifying x = -74.641016151Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.358983849, -74.641016151}
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