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Simplifying 1845 = 4500x + -8x2 Solving 1845 = 4500x + -8x2 Solving for variable 'x'. Reorder the terms: 1845 + -4500x + 8x2 = 4500x + -4500x + -8x2 + 8x2 Combine like terms: 4500x + -4500x = 0 1845 + -4500x + 8x2 = 0 + -8x2 + 8x2 1845 + -4500x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 1845 + -4500x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 230.625 + -562.5x + x2 = 0 Move the constant term to the right: Add '-230.625' to each side of the equation. 230.625 + -562.5x + -230.625 + x2 = 0 + -230.625 Reorder the terms: 230.625 + -230.625 + -562.5x + x2 = 0 + -230.625 Combine like terms: 230.625 + -230.625 = 0.000 0.000 + -562.5x + x2 = 0 + -230.625 -562.5x + x2 = 0 + -230.625 Combine like terms: 0 + -230.625 = -230.625 -562.5x + x2 = -230.625 The x term is -562.5x. Take half its coefficient (-281.25). Square it (79101.5625) and add it to both sides. Add '79101.5625' to each side of the equation. -562.5x + 79101.5625 + x2 = -230.625 + 79101.5625 Reorder the terms: 79101.5625 + -562.5x + x2 = -230.625 + 79101.5625 Combine like terms: -230.625 + 79101.5625 = 78870.9375 79101.5625 + -562.5x + x2 = 78870.9375 Factor a perfect square on the left side: (x + -281.25)(x + -281.25) = 78870.9375 Calculate the square root of the right side: 280.839700719 Break this problem into two subproblems by setting (x + -281.25) equal to 280.839700719 and -280.839700719.Subproblem 1
x + -281.25 = 280.839700719 Simplifying x + -281.25 = 280.839700719 Reorder the terms: -281.25 + x = 280.839700719 Solving -281.25 + x = 280.839700719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '281.25' to each side of the equation. -281.25 + 281.25 + x = 280.839700719 + 281.25 Combine like terms: -281.25 + 281.25 = 0.00 0.00 + x = 280.839700719 + 281.25 x = 280.839700719 + 281.25 Combine like terms: 280.839700719 + 281.25 = 562.089700719 x = 562.089700719 Simplifying x = 562.089700719Subproblem 2
x + -281.25 = -280.839700719 Simplifying x + -281.25 = -280.839700719 Reorder the terms: -281.25 + x = -280.839700719 Solving -281.25 + x = -280.839700719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '281.25' to each side of the equation. -281.25 + 281.25 + x = -280.839700719 + 281.25 Combine like terms: -281.25 + 281.25 = 0.00 0.00 + x = -280.839700719 + 281.25 x = -280.839700719 + 281.25 Combine like terms: -280.839700719 + 281.25 = 0.410299281 x = 0.410299281 Simplifying x = 0.410299281Solution
The solution to the problem is based on the solutions from the subproblems. x = {562.089700719, 0.410299281}
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