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Simplifying 61.25 = 350x + -500x2 Solving 61.25 = 350x + -500x2 Solving for variable 'x'. Reorder the terms: 61.25 + -350x + 500x2 = 350x + -350x + -500x2 + 500x2 Combine like terms: 350x + -350x = 0 61.25 + -350x + 500x2 = 0 + -500x2 + 500x2 61.25 + -350x + 500x2 = -500x2 + 500x2 Combine like terms: -500x2 + 500x2 = 0 61.25 + -350x + 500x2 = 0 Begin completing the square. Divide all terms by 500 the coefficient of the squared term: Divide each side by '500'. 0.1225 + -0.7x + x2 = 0 Move the constant term to the right: Add '-0.1225' to each side of the equation. 0.1225 + -0.7x + -0.1225 + x2 = 0 + -0.1225 Reorder the terms: 0.1225 + -0.1225 + -0.7x + x2 = 0 + -0.1225 Combine like terms: 0.1225 + -0.1225 = 0.0000 0.0000 + -0.7x + x2 = 0 + -0.1225 -0.7x + x2 = 0 + -0.1225 Combine like terms: 0 + -0.1225 = -0.1225 -0.7x + x2 = -0.1225 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = -0.1225 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = -0.1225 + 0.1225 Combine like terms: -0.1225 + 0.1225 = 0.0000 0.1225 + -0.7x + x2 = 0.0000 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -0.35) equal to 0.0000 and 0.0000.Subproblem 1
x + -0.35 = 0.0000 Simplifying x + -0.35 = 0.0000 Reorder the terms: -0.35 + x = 0.0000 Solving -0.35 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.0000 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.0000 + 0.35 x = 0.0000 + 0.35 Combine like terms: 0.0000 + 0.35 = 0.35 x = 0.35 Simplifying x = 0.35Subproblem 2
x + -0.35 = 0.0000 Simplifying x + -0.35 = 0.0000 Reorder the terms: -0.35 + x = 0.0000 Solving -0.35 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 0.0000 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.0000 + 0.35 x = 0.0000 + 0.35 Combine like terms: 0.0000 + 0.35 = 0.35 x = 0.35 Simplifying x = 0.35Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.35, 0.35}
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