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Simplifying -1x2 + 860x + -2500 = 0 Reorder the terms: -2500 + 860x + -1x2 = 0 Solving -2500 + 860x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2500 + -860x + x2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -860x + -2500 + x2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -860x + x2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -860x + x2 = 0 + -2500 -860x + x2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -860x + x2 = -2500 The x term is -860x. Take half its coefficient (-430). Square it (184900) and add it to both sides. Add '184900' to each side of the equation. -860x + 184900 + x2 = -2500 + 184900 Reorder the terms: 184900 + -860x + x2 = -2500 + 184900 Combine like terms: -2500 + 184900 = 182400 184900 + -860x + x2 = 182400 Factor a perfect square on the left side: (x + -430)(x + -430) = 182400 Calculate the square root of the right side: 427.083130081 Break this problem into two subproblems by setting (x + -430) equal to 427.083130081 and -427.083130081.Subproblem 1
x + -430 = 427.083130081 Simplifying x + -430 = 427.083130081 Reorder the terms: -430 + x = 427.083130081 Solving -430 + x = 427.083130081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '430' to each side of the equation. -430 + 430 + x = 427.083130081 + 430 Combine like terms: -430 + 430 = 0 0 + x = 427.083130081 + 430 x = 427.083130081 + 430 Combine like terms: 427.083130081 + 430 = 857.083130081 x = 857.083130081 Simplifying x = 857.083130081Subproblem 2
x + -430 = -427.083130081 Simplifying x + -430 = -427.083130081 Reorder the terms: -430 + x = -427.083130081 Solving -430 + x = -427.083130081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '430' to each side of the equation. -430 + 430 + x = -427.083130081 + 430 Combine like terms: -430 + 430 = 0 0 + x = -427.083130081 + 430 x = -427.083130081 + 430 Combine like terms: -427.083130081 + 430 = 2.916869919 x = 2.916869919 Simplifying x = 2.916869919Solution
The solution to the problem is based on the solutions from the subproblems. x = {857.083130081, 2.916869919}
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