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Simplifying 0.03x2 + -33x + 15000 = 7800 Reorder the terms: 15000 + -33x + 0.03x2 = 7800 Solving 15000 + -33x + 0.03x2 = 7800 Solving for variable 'x'. Reorder the terms: 15000 + -7800 + -33x + 0.03x2 = 7800 + -7800 Combine like terms: 15000 + -7800 = 7200 7200 + -33x + 0.03x2 = 7800 + -7800 Combine like terms: 7800 + -7800 = 0 7200 + -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'. 240000 + -1100x + x2 = 0 Move the constant term to the right: Add '-240000' to each side of the equation. 240000 + -1100x + -240000 + x2 = 0 + -240000 Reorder the terms: 240000 + -240000 + -1100x + x2 = 0 + -240000 Combine like terms: 240000 + -240000 = 0 0 + -1100x + x2 = 0 + -240000 -1100x + x2 = 0 + -240000 Combine like terms: 0 + -240000 = -240000 -1100x + x2 = -240000 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 = -240000 + 302500 Reorder the terms: 302500 + -1100x + x2 = -240000 + 302500 Combine like terms: -240000 + 302500 = 62500 302500 + -1100x + x2 = 62500 Factor a perfect square on the left side: (x + -550)(x + -550) = 62500 Calculate the square root of the right side: 250 Break this problem into two subproblems by setting (x + -550) equal to 250 and -250.Subproblem 1
x + -550 = 250 Simplifying x + -550 = 250 Reorder the terms: -550 + x = 250 Solving -550 + x = 250 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 = 250 + 550 Combine like terms: -550 + 550 = 0 0 + x = 250 + 550 x = 250 + 550 Combine like terms: 250 + 550 = 800 x = 800 Simplifying x = 800Subproblem 2
x + -550 = -250 Simplifying x + -550 = -250 Reorder the terms: -550 + x = -250 Solving -550 + x = -250 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 = -250 + 550 Combine like terms: -550 + 550 = 0 0 + x = -250 + 550 x = -250 + 550 Combine like terms: -250 + 550 = 300 x = 300 Simplifying x = 300Solution
The solution to the problem is based on the solutions from the subproblems. x = {800, 300}
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