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Simplifying 4x2 + -725x + 625 = 0 Reorder the terms: 625 + -725x + 4x2 = 0 Solving 625 + -725x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 156.25 + -181.25x + x2 = 0 Move the constant term to the right: Add '-156.25' to each side of the equation. 156.25 + -181.25x + -156.25 + x2 = 0 + -156.25 Reorder the terms: 156.25 + -156.25 + -181.25x + x2 = 0 + -156.25 Combine like terms: 156.25 + -156.25 = 0.00 0.00 + -181.25x + x2 = 0 + -156.25 -181.25x + x2 = 0 + -156.25 Combine like terms: 0 + -156.25 = -156.25 -181.25x + x2 = -156.25 The x term is -181.25x. Take half its coefficient (-90.625). Square it (8212.890625) and add it to both sides. Add '8212.890625' to each side of the equation. -181.25x + 8212.890625 + x2 = -156.25 + 8212.890625 Reorder the terms: 8212.890625 + -181.25x + x2 = -156.25 + 8212.890625 Combine like terms: -156.25 + 8212.890625 = 8056.640625 8212.890625 + -181.25x + x2 = 8056.640625 Factor a perfect square on the left side: (x + -90.625)(x + -90.625) = 8056.640625 Calculate the square root of the right side: 89.758791352 Break this problem into two subproblems by setting (x + -90.625) equal to 89.758791352 and -89.758791352.Subproblem 1
x + -90.625 = 89.758791352 Simplifying x + -90.625 = 89.758791352 Reorder the terms: -90.625 + x = 89.758791352 Solving -90.625 + x = 89.758791352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90.625' to each side of the equation. -90.625 + 90.625 + x = 89.758791352 + 90.625 Combine like terms: -90.625 + 90.625 = 0.000 0.000 + x = 89.758791352 + 90.625 x = 89.758791352 + 90.625 Combine like terms: 89.758791352 + 90.625 = 180.383791352 x = 180.383791352 Simplifying x = 180.383791352Subproblem 2
x + -90.625 = -89.758791352 Simplifying x + -90.625 = -89.758791352 Reorder the terms: -90.625 + x = -89.758791352 Solving -90.625 + x = -89.758791352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90.625' to each side of the equation. -90.625 + 90.625 + x = -89.758791352 + 90.625 Combine like terms: -90.625 + 90.625 = 0.000 0.000 + x = -89.758791352 + 90.625 x = -89.758791352 + 90.625 Combine like terms: -89.758791352 + 90.625 = 0.866208648 x = 0.866208648 Simplifying x = 0.866208648Solution
The solution to the problem is based on the solutions from the subproblems. x = {180.383791352, 0.866208648}
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