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Simplifying x(x + 111.50) = 4791.50 Reorder the terms: x(111.50 + x) = 4791.50 (111.50 * x + x * x) = 4791.50 (111.50x + x2) = 4791.50 Solving 111.50x + x2 = 4791.50 Solving for variable 'x'. Reorder the terms: -4791.50 + 111.50x + x2 = 4791.50 + -4791.50 Combine like terms: 4791.50 + -4791.50 = 0.00 -4791.50 + 111.50x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '4791.50' to each side of the equation. -4791.50 + 111.50x + 4791.50 + x2 = 0.00 + 4791.50 Reorder the terms: -4791.50 + 4791.50 + 111.50x + x2 = 0.00 + 4791.50 Combine like terms: -4791.50 + 4791.50 = 0.00 0.00 + 111.50x + x2 = 0.00 + 4791.50 111.50x + x2 = 0.00 + 4791.50 Combine like terms: 0.00 + 4791.50 = 4791.5 111.50x + x2 = 4791.5 The x term is 111.50x. Take half its coefficient (55.75). Square it (3108.0625) and add it to both sides. Add '3108.0625' to each side of the equation. 111.50x + 3108.0625 + x2 = 4791.5 + 3108.0625 Reorder the terms: 3108.0625 + 111.50x + x2 = 4791.5 + 3108.0625 Combine like terms: 4791.5 + 3108.0625 = 7899.5625 3108.0625 + 111.50x + x2 = 7899.5625 Factor a perfect square on the left side: (x + 55.75)(x + 55.75) = 7899.5625 Calculate the square root of the right side: 88.879483009 Break this problem into two subproblems by setting (x + 55.75) equal to 88.879483009 and -88.879483009.Subproblem 1
x + 55.75 = 88.879483009 Simplifying x + 55.75 = 88.879483009 Reorder the terms: 55.75 + x = 88.879483009 Solving 55.75 + x = 88.879483009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.75' to each side of the equation. 55.75 + -55.75 + x = 88.879483009 + -55.75 Combine like terms: 55.75 + -55.75 = 0.00 0.00 + x = 88.879483009 + -55.75 x = 88.879483009 + -55.75 Combine like terms: 88.879483009 + -55.75 = 33.129483009 x = 33.129483009 Simplifying x = 33.129483009Subproblem 2
x + 55.75 = -88.879483009 Simplifying x + 55.75 = -88.879483009 Reorder the terms: 55.75 + x = -88.879483009 Solving 55.75 + x = -88.879483009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55.75' to each side of the equation. 55.75 + -55.75 + x = -88.879483009 + -55.75 Combine like terms: 55.75 + -55.75 = 0.00 0.00 + x = -88.879483009 + -55.75 x = -88.879483009 + -55.75 Combine like terms: -88.879483009 + -55.75 = -144.629483009 x = -144.629483009 Simplifying x = -144.629483009Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.129483009, -144.629483009}
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