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Simplifying x(35 + -0.01x) + -2x + 500 = 0 (35 * x + -0.01x * x) + -2x + 500 = 0 (35x + -0.01x2) + -2x + 500 = 0 Reorder the terms: 500 + 35x + -2x + -0.01x2 = 0 Combine like terms: 35x + -2x = 33x 500 + 33x + -0.01x2 = 0 Solving 500 + 33x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -50000 + -3300x + x2 = 0 Move the constant term to the right: Add '50000' to each side of the equation. -50000 + -3300x + 50000 + x2 = 0 + 50000 Reorder the terms: -50000 + 50000 + -3300x + x2 = 0 + 50000 Combine like terms: -50000 + 50000 = 0 0 + -3300x + x2 = 0 + 50000 -3300x + x2 = 0 + 50000 Combine like terms: 0 + 50000 = 50000 -3300x + x2 = 50000 The x term is -3300x. Take half its coefficient (-1650). Square it (2722500) and add it to both sides. Add '2722500' to each side of the equation. -3300x + 2722500 + x2 = 50000 + 2722500 Reorder the terms: 2722500 + -3300x + x2 = 50000 + 2722500 Combine like terms: 50000 + 2722500 = 2772500 2722500 + -3300x + x2 = 2772500 Factor a perfect square on the left side: (x + -1650)(x + -1650) = 2772500 Calculate the square root of the right side: 1665.082580535 Break this problem into two subproblems by setting (x + -1650) equal to 1665.082580535 and -1665.082580535.Subproblem 1
x + -1650 = 1665.082580535 Simplifying x + -1650 = 1665.082580535 Reorder the terms: -1650 + x = 1665.082580535 Solving -1650 + x = 1665.082580535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1650' to each side of the equation. -1650 + 1650 + x = 1665.082580535 + 1650 Combine like terms: -1650 + 1650 = 0 0 + x = 1665.082580535 + 1650 x = 1665.082580535 + 1650 Combine like terms: 1665.082580535 + 1650 = 3315.082580535 x = 3315.082580535 Simplifying x = 3315.082580535Subproblem 2
x + -1650 = -1665.082580535 Simplifying x + -1650 = -1665.082580535 Reorder the terms: -1650 + x = -1665.082580535 Solving -1650 + x = -1665.082580535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1650' to each side of the equation. -1650 + 1650 + x = -1665.082580535 + 1650 Combine like terms: -1650 + 1650 = 0 0 + x = -1665.082580535 + 1650 x = -1665.082580535 + 1650 Combine like terms: -1665.082580535 + 1650 = -15.082580535 x = -15.082580535 Simplifying x = -15.082580535Solution
The solution to the problem is based on the solutions from the subproblems. x = {3315.082580535, -15.082580535}
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