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Simplifying 3x2 + 25 = x2 + 75x Reorder the terms: 25 + 3x2 = x2 + 75x Reorder the terms: 25 + 3x2 = 75x + x2 Solving 25 + 3x2 = 75x + x2 Solving for variable 'x'. Reorder the terms: 25 + -75x + 3x2 + -1x2 = 75x + x2 + -75x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 25 + -75x + 2x2 = 75x + x2 + -75x + -1x2 Reorder the terms: 25 + -75x + 2x2 = 75x + -75x + x2 + -1x2 Combine like terms: 75x + -75x = 0 25 + -75x + 2x2 = 0 + x2 + -1x2 25 + -75x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + -75x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -37.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -37.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -37.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -37.5x + x2 = 0 + -12.5 -37.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -37.5x + x2 = -12.5 The x term is -37.5x. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5x + 351.5625 + x2 = -12.5 + 351.5625 Reorder the terms: 351.5625 + -37.5x + x2 = -12.5 + 351.5625 Combine like terms: -12.5 + 351.5625 = 339.0625 351.5625 + -37.5x + x2 = 339.0625 Factor a perfect square on the left side: (x + -18.75)(x + -18.75) = 339.0625 Calculate the square root of the right side: 18.413649828 Break this problem into two subproblems by setting (x + -18.75) equal to 18.413649828 and -18.413649828.Subproblem 1
x + -18.75 = 18.413649828 Simplifying x + -18.75 = 18.413649828 Reorder the terms: -18.75 + x = 18.413649828 Solving -18.75 + x = 18.413649828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = 18.413649828 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 18.413649828 + 18.75 x = 18.413649828 + 18.75 Combine like terms: 18.413649828 + 18.75 = 37.163649828 x = 37.163649828 Simplifying x = 37.163649828Subproblem 2
x + -18.75 = -18.413649828 Simplifying x + -18.75 = -18.413649828 Reorder the terms: -18.75 + x = -18.413649828 Solving -18.75 + x = -18.413649828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = -18.413649828 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = -18.413649828 + 18.75 x = -18.413649828 + 18.75 Combine like terms: -18.413649828 + 18.75 = 0.336350172 x = 0.336350172 Simplifying x = 0.336350172Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.163649828, 0.336350172}
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