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Simplifying x(35 + -0.01x) + -25x + 500 = 0 (35 * x + -0.01x * x) + -25x + 500 = 0 (35x + -0.01x2) + -25x + 500 = 0 Reorder the terms: 500 + 35x + -25x + -0.01x2 = 0 Combine like terms: 35x + -25x = 10x 500 + 10x + -0.01x2 = 0 Solving 500 + 10x + -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 + -1000x + x2 = 0 Move the constant term to the right: Add '50000' to each side of the equation. -50000 + -1000x + 50000 + x2 = 0 + 50000 Reorder the terms: -50000 + 50000 + -1000x + x2 = 0 + 50000 Combine like terms: -50000 + 50000 = 0 0 + -1000x + x2 = 0 + 50000 -1000x + x2 = 0 + 50000 Combine like terms: 0 + 50000 = 50000 -1000x + x2 = 50000 The x term is -1000x. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000x + 250000 + x2 = 50000 + 250000 Reorder the terms: 250000 + -1000x + x2 = 50000 + 250000 Combine like terms: 50000 + 250000 = 300000 250000 + -1000x + x2 = 300000 Factor a perfect square on the left side: (x + -500)(x + -500) = 300000 Calculate the square root of the right side: 547.722557505 Break this problem into two subproblems by setting (x + -500) equal to 547.722557505 and -547.722557505.Subproblem 1
x + -500 = 547.722557505 Simplifying x + -500 = 547.722557505 Reorder the terms: -500 + x = 547.722557505 Solving -500 + x = 547.722557505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 547.722557505 + 500 Combine like terms: -500 + 500 = 0 0 + x = 547.722557505 + 500 x = 547.722557505 + 500 Combine like terms: 547.722557505 + 500 = 1047.722557505 x = 1047.722557505 Simplifying x = 1047.722557505Subproblem 2
x + -500 = -547.722557505 Simplifying x + -500 = -547.722557505 Reorder the terms: -500 + x = -547.722557505 Solving -500 + x = -547.722557505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -547.722557505 + 500 Combine like terms: -500 + 500 = 0 0 + x = -547.722557505 + 500 x = -547.722557505 + 500 Combine like terms: -547.722557505 + 500 = -47.722557505 x = -47.722557505 Simplifying x = -47.722557505Solution
The solution to the problem is based on the solutions from the subproblems. x = {1047.722557505, -47.722557505}
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