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Simplifying 17000 = -0.75x2 + 255x + -1000 Reorder the terms: 17000 = -1000 + 255x + -0.75x2 Solving 17000 = -1000 + 255x + -0.75x2 Solving for variable 'x'. Combine like terms: 17000 + 1000 = 18000 18000 + -255x + 0.75x2 = -1000 + 255x + -0.75x2 + 1000 + -255x + 0.75x2 Reorder the terms: 18000 + -255x + 0.75x2 = -1000 + 1000 + 255x + -255x + -0.75x2 + 0.75x2 Combine like terms: -1000 + 1000 = 0 18000 + -255x + 0.75x2 = 0 + 255x + -255x + -0.75x2 + 0.75x2 18000 + -255x + 0.75x2 = 255x + -255x + -0.75x2 + 0.75x2 Combine like terms: 255x + -255x = 0 18000 + -255x + 0.75x2 = 0 + -0.75x2 + 0.75x2 18000 + -255x + 0.75x2 = -0.75x2 + 0.75x2 Combine like terms: -0.75x2 + 0.75x2 = 0.00 18000 + -255x + 0.75x2 = 0.00 Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. 24000 + -340x + x2 = 0 Move the constant term to the right: Add '-24000' to each side of the equation. 24000 + -340x + -24000 + x2 = 0 + -24000 Reorder the terms: 24000 + -24000 + -340x + x2 = 0 + -24000 Combine like terms: 24000 + -24000 = 0 0 + -340x + x2 = 0 + -24000 -340x + x2 = 0 + -24000 Combine like terms: 0 + -24000 = -24000 -340x + x2 = -24000 The x term is -340x. Take half its coefficient (-170). Square it (28900) and add it to both sides. Add '28900' to each side of the equation. -340x + 28900 + x2 = -24000 + 28900 Reorder the terms: 28900 + -340x + x2 = -24000 + 28900 Combine like terms: -24000 + 28900 = 4900 28900 + -340x + x2 = 4900 Factor a perfect square on the left side: (x + -170)(x + -170) = 4900 Calculate the square root of the right side: 70 Break this problem into two subproblems by setting (x + -170) equal to 70 and -70.Subproblem 1
x + -170 = 70 Simplifying x + -170 = 70 Reorder the terms: -170 + x = 70 Solving -170 + x = 70 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '170' to each side of the equation. -170 + 170 + x = 70 + 170 Combine like terms: -170 + 170 = 0 0 + x = 70 + 170 x = 70 + 170 Combine like terms: 70 + 170 = 240 x = 240 Simplifying x = 240Subproblem 2
x + -170 = -70 Simplifying x + -170 = -70 Reorder the terms: -170 + x = -70 Solving -170 + x = -70 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '170' to each side of the equation. -170 + 170 + x = -70 + 170 Combine like terms: -170 + 170 = 0 0 + x = -70 + 170 x = -70 + 170 Combine like terms: -70 + 170 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {240, 100}
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