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Simplifying 22800 = 0.03x2 + -33x + 15000 Reorder the terms: 22800 = 15000 + -33x + 0.03x2 Solving 22800 = 15000 + -33x + 0.03x2 Solving for variable 'x'. Combine like terms: 22800 + -15000 = 7800 7800 + 33x + -0.03x2 = 15000 + -33x + 0.03x2 + -15000 + 33x + -0.03x2 Reorder the terms: 7800 + 33x + -0.03x2 = 15000 + -15000 + -33x + 33x + 0.03x2 + -0.03x2 Combine like terms: 15000 + -15000 = 0 7800 + 33x + -0.03x2 = 0 + -33x + 33x + 0.03x2 + -0.03x2 7800 + 33x + -0.03x2 = -33x + 33x + 0.03x2 + -0.03x2 Combine like terms: -33x + 33x = 0 7800 + 33x + -0.03x2 = 0 + 0.03x2 + -0.03x2 7800 + 33x + -0.03x2 = 0.03x2 + -0.03x2 Combine like terms: 0.03x2 + -0.03x2 = 0.00 7800 + 33x + -0.03x2 = 0.00 Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. -260000 + -1100x + x2 = 0 Move the constant term to the right: Add '260000' to each side of the equation. -260000 + -1100x + 260000 + x2 = 0 + 260000 Reorder the terms: -260000 + 260000 + -1100x + x2 = 0 + 260000 Combine like terms: -260000 + 260000 = 0 0 + -1100x + x2 = 0 + 260000 -1100x + x2 = 0 + 260000 Combine like terms: 0 + 260000 = 260000 -1100x + x2 = 260000 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 = 260000 + 302500 Reorder the terms: 302500 + -1100x + x2 = 260000 + 302500 Combine like terms: 260000 + 302500 = 562500 302500 + -1100x + x2 = 562500 Factor a perfect square on the left side: (x + -550)(x + -550) = 562500 Calculate the square root of the right side: 750 Break this problem into two subproblems by setting (x + -550) equal to 750 and -750.Subproblem 1
x + -550 = 750 Simplifying x + -550 = 750 Reorder the terms: -550 + x = 750 Solving -550 + x = 750 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 = 750 + 550 Combine like terms: -550 + 550 = 0 0 + x = 750 + 550 x = 750 + 550 Combine like terms: 750 + 550 = 1300 x = 1300 Simplifying x = 1300Subproblem 2
x + -550 = -750 Simplifying x + -550 = -750 Reorder the terms: -550 + x = -750 Solving -550 + x = -750 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 = -750 + 550 Combine like terms: -550 + 550 = 0 0 + x = -750 + 550 x = -750 + 550 Combine like terms: -750 + 550 = -200 x = -200 Simplifying x = -200Solution
The solution to the problem is based on the solutions from the subproblems. x = {1300, -200}
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