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Simplifying 25x2 + -60x = -31 Reorder the terms: -60x + 25x2 = -31 Solving -60x + 25x2 = -31 Solving for variable 'x'. Reorder the terms: 31 + -60x + 25x2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + -60x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.24 + -2.4x + x2 = 0 Move the constant term to the right: Add '-1.24' to each side of the equation. 1.24 + -2.4x + -1.24 + x2 = 0 + -1.24 Reorder the terms: 1.24 + -1.24 + -2.4x + x2 = 0 + -1.24 Combine like terms: 1.24 + -1.24 = 0.00 0.00 + -2.4x + x2 = 0 + -1.24 -2.4x + x2 = 0 + -1.24 Combine like terms: 0 + -1.24 = -1.24 -2.4x + x2 = -1.24 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -1.24 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -1.24 + 1.44 Combine like terms: -1.24 + 1.44 = 0.2 1.44 + -2.4x + x2 = 0.2 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + -1.2) equal to 0.447213596 and -0.447213596.Subproblem 1
x + -1.2 = 0.447213596 Simplifying x + -1.2 = 0.447213596 Reorder the terms: -1.2 + x = 0.447213596 Solving -1.2 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.447213596 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.447213596 + 1.2 x = 0.447213596 + 1.2 Combine like terms: 0.447213596 + 1.2 = 1.647213596 x = 1.647213596 Simplifying x = 1.647213596Subproblem 2
x + -1.2 = -0.447213596 Simplifying x + -1.2 = -0.447213596 Reorder the terms: -1.2 + x = -0.447213596 Solving -1.2 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.447213596 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.447213596 + 1.2 x = -0.447213596 + 1.2 Combine like terms: -0.447213596 + 1.2 = 0.752786404 x = 0.752786404 Simplifying x = 0.752786404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.647213596, 0.752786404}
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