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Simplifying 35 = 0.01x2 + 5x Reorder the terms: 35 = 5x + 0.01x2 Solving 35 = 5x + 0.01x2 Solving for variable 'x'. Reorder the terms: 35 + -5x + -0.01x2 = 5x + -5x + 0.01x2 + -0.01x2 Combine like terms: 5x + -5x = 0 35 + -5x + -0.01x2 = 0 + 0.01x2 + -0.01x2 35 + -5x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 35 + -5x + -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'. -3500 + 500x + x2 = 0 Move the constant term to the right: Add '3500' to each side of the equation. -3500 + 500x + 3500 + x2 = 0 + 3500 Reorder the terms: -3500 + 3500 + 500x + x2 = 0 + 3500 Combine like terms: -3500 + 3500 = 0 0 + 500x + x2 = 0 + 3500 500x + x2 = 0 + 3500 Combine like terms: 0 + 3500 = 3500 500x + x2 = 3500 The x term is 500x. Take half its coefficient (250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. 500x + 62500 + x2 = 3500 + 62500 Reorder the terms: 62500 + 500x + x2 = 3500 + 62500 Combine like terms: 3500 + 62500 = 66000 62500 + 500x + x2 = 66000 Factor a perfect square on the left side: (x + 250)(x + 250) = 66000 Calculate the square root of the right side: 256.904651573 Break this problem into two subproblems by setting (x + 250) equal to 256.904651573 and -256.904651573.Subproblem 1
x + 250 = 256.904651573 Simplifying x + 250 = 256.904651573 Reorder the terms: 250 + x = 256.904651573 Solving 250 + x = 256.904651573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 256.904651573 + -250 Combine like terms: 250 + -250 = 0 0 + x = 256.904651573 + -250 x = 256.904651573 + -250 Combine like terms: 256.904651573 + -250 = 6.904651573 x = 6.904651573 Simplifying x = 6.904651573Subproblem 2
x + 250 = -256.904651573 Simplifying x + 250 = -256.904651573 Reorder the terms: 250 + x = -256.904651573 Solving 250 + x = -256.904651573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -256.904651573 + -250 Combine like terms: 250 + -250 = 0 0 + x = -256.904651573 + -250 x = -256.904651573 + -250 Combine like terms: -256.904651573 + -250 = -506.904651573 x = -506.904651573 Simplifying x = -506.904651573Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.904651573, -506.904651573}
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