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Simplifying 0.03X2 + -33X + 15000 = 28000 Reorder the terms: 15000 + -33X + 0.03X2 = 28000 Solving 15000 + -33X + 0.03X2 = 28000 Solving for variable 'X'. Reorder the terms: 15000 + -28000 + -33X + 0.03X2 = 28000 + -28000 Combine like terms: 15000 + -28000 = -13000 -13000 + -33X + 0.03X2 = 28000 + -28000 Combine like terms: 28000 + -28000 = 0 -13000 + -33X + 0.03X2 = 0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. -433333.3333 + -1100X + X2 = 0 Move the constant term to the right: Add '433333.3333' to each side of the equation. -433333.3333 + -1100X + 433333.3333 + X2 = 0 + 433333.3333 Reorder the terms: -433333.3333 + 433333.3333 + -1100X + X2 = 0 + 433333.3333 Combine like terms: -433333.3333 + 433333.3333 = 0.0000 0.0000 + -1100X + X2 = 0 + 433333.3333 -1100X + X2 = 0 + 433333.3333 Combine like terms: 0 + 433333.3333 = 433333.3333 -1100X + X2 = 433333.3333 The X term is -1100X. Take half its coefficient (-550). Square it (302500) and add it to both sides. Add '302500' to each side of the equation. -1100X + 302500 + X2 = 433333.3333 + 302500 Reorder the terms: 302500 + -1100X + X2 = 433333.3333 + 302500 Combine like terms: 433333.3333 + 302500 = 735833.3333 302500 + -1100X + X2 = 735833.3333 Factor a perfect square on the left side: (X + -550)(X + -550) = 735833.3333 Calculate the square root of the right side: 857.807282144 Break this problem into two subproblems by setting (X + -550) equal to 857.807282144 and -857.807282144.Subproblem 1
X + -550 = 857.807282144 Simplifying X + -550 = 857.807282144 Reorder the terms: -550 + X = 857.807282144 Solving -550 + X = 857.807282144 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + X = 857.807282144 + 550 Combine like terms: -550 + 550 = 0 0 + X = 857.807282144 + 550 X = 857.807282144 + 550 Combine like terms: 857.807282144 + 550 = 1407.807282144 X = 1407.807282144 Simplifying X = 1407.807282144Subproblem 2
X + -550 = -857.807282144 Simplifying X + -550 = -857.807282144 Reorder the terms: -550 + X = -857.807282144 Solving -550 + X = -857.807282144 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + X = -857.807282144 + 550 Combine like terms: -550 + 550 = 0 0 + X = -857.807282144 + 550 X = -857.807282144 + 550 Combine like terms: -857.807282144 + 550 = -307.807282144 X = -307.807282144 Simplifying X = -307.807282144Solution
The solution to the problem is based on the solutions from the subproblems. X = {1407.807282144, -307.807282144}
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