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Simplifying 250x + -1x2 = 7200 Solving 250x + -1x2 = 7200 Solving for variable 'x'. Reorder the terms: -7200 + 250x + -1x2 = 7200 + -7200 Combine like terms: 7200 + -7200 = 0 -7200 + 250x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7200 + -250x + x2 = 0 Move the constant term to the right: Add '-7200' to each side of the equation. 7200 + -250x + -7200 + x2 = 0 + -7200 Reorder the terms: 7200 + -7200 + -250x + x2 = 0 + -7200 Combine like terms: 7200 + -7200 = 0 0 + -250x + x2 = 0 + -7200 -250x + x2 = 0 + -7200 Combine like terms: 0 + -7200 = -7200 -250x + x2 = -7200 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = -7200 + 15625 Reorder the terms: 15625 + -250x + x2 = -7200 + 15625 Combine like terms: -7200 + 15625 = 8425 15625 + -250x + x2 = 8425 Factor a perfect square on the left side: (x + -125)(x + -125) = 8425 Calculate the square root of the right side: 91.787798753 Break this problem into two subproblems by setting (x + -125) equal to 91.787798753 and -91.787798753.Subproblem 1
x + -125 = 91.787798753 Simplifying x + -125 = 91.787798753 Reorder the terms: -125 + x = 91.787798753 Solving -125 + x = 91.787798753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 91.787798753 + 125 Combine like terms: -125 + 125 = 0 0 + x = 91.787798753 + 125 x = 91.787798753 + 125 Combine like terms: 91.787798753 + 125 = 216.787798753 x = 216.787798753 Simplifying x = 216.787798753Subproblem 2
x + -125 = -91.787798753 Simplifying x + -125 = -91.787798753 Reorder the terms: -125 + x = -91.787798753 Solving -125 + x = -91.787798753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -91.787798753 + 125 Combine like terms: -125 + 125 = 0 0 + x = -91.787798753 + 125 x = -91.787798753 + 125 Combine like terms: -91.787798753 + 125 = 33.212201247 x = 33.212201247 Simplifying x = 33.212201247Solution
The solution to the problem is based on the solutions from the subproblems. x = {216.787798753, 33.212201247}
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