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Simplifying 150x = 3000 + 10x + 0.2x2 Solving 150x = 3000 + 10x + 0.2x2 Solving for variable 'x'. Reorder the terms: -3000 + 150x + -10x + -0.2x2 = 3000 + 10x + 0.2x2 + -3000 + -10x + -0.2x2 Combine like terms: 150x + -10x = 140x -3000 + 140x + -0.2x2 = 3000 + 10x + 0.2x2 + -3000 + -10x + -0.2x2 Reorder the terms: -3000 + 140x + -0.2x2 = 3000 + -3000 + 10x + -10x + 0.2x2 + -0.2x2 Combine like terms: 3000 + -3000 = 0 -3000 + 140x + -0.2x2 = 0 + 10x + -10x + 0.2x2 + -0.2x2 -3000 + 140x + -0.2x2 = 10x + -10x + 0.2x2 + -0.2x2 Combine like terms: 10x + -10x = 0 -3000 + 140x + -0.2x2 = 0 + 0.2x2 + -0.2x2 -3000 + 140x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 -3000 + 140x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 15000 + -700x + x2 = 0 Move the constant term to the right: Add '-15000' to each side of the equation. 15000 + -700x + -15000 + x2 = 0 + -15000 Reorder the terms: 15000 + -15000 + -700x + x2 = 0 + -15000 Combine like terms: 15000 + -15000 = 0 0 + -700x + x2 = 0 + -15000 -700x + x2 = 0 + -15000 Combine like terms: 0 + -15000 = -15000 -700x + x2 = -15000 The x term is -700x. Take half its coefficient (-350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. -700x + 122500 + x2 = -15000 + 122500 Reorder the terms: 122500 + -700x + x2 = -15000 + 122500 Combine like terms: -15000 + 122500 = 107500 122500 + -700x + x2 = 107500 Factor a perfect square on the left side: (x + -350)(x + -350) = 107500 Calculate the square root of the right side: 327.871926215 Break this problem into two subproblems by setting (x + -350) equal to 327.871926215 and -327.871926215.Subproblem 1
x + -350 = 327.871926215 Simplifying x + -350 = 327.871926215 Reorder the terms: -350 + x = 327.871926215 Solving -350 + x = 327.871926215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = 327.871926215 + 350 Combine like terms: -350 + 350 = 0 0 + x = 327.871926215 + 350 x = 327.871926215 + 350 Combine like terms: 327.871926215 + 350 = 677.871926215 x = 677.871926215 Simplifying x = 677.871926215Subproblem 2
x + -350 = -327.871926215 Simplifying x + -350 = -327.871926215 Reorder the terms: -350 + x = -327.871926215 Solving -350 + x = -327.871926215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '350' to each side of the equation. -350 + 350 + x = -327.871926215 + 350 Combine like terms: -350 + 350 = 0 0 + x = -327.871926215 + 350 x = -327.871926215 + 350 Combine like terms: -327.871926215 + 350 = 22.128073785 x = 22.128073785 Simplifying x = 22.128073785Solution
The solution to the problem is based on the solutions from the subproblems. x = {677.871926215, 22.128073785}
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