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Simplifying 96x2 + -120x + 25 = 0 Reorder the terms: 25 + -120x + 96x2 = 0 Solving 25 + -120x + 96x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. 0.2604166667 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.2604166667' to each side of the equation. 0.2604166667 + -1.25x + -0.2604166667 + x2 = 0 + -0.2604166667 Reorder the terms: 0.2604166667 + -0.2604166667 + -1.25x + x2 = 0 + -0.2604166667 Combine like terms: 0.2604166667 + -0.2604166667 = 0.0000000000 0.0000000000 + -1.25x + x2 = 0 + -0.2604166667 -1.25x + x2 = 0 + -0.2604166667 Combine like terms: 0 + -0.2604166667 = -0.2604166667 -1.25x + x2 = -0.2604166667 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.2604166667 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.2604166667 + 0.390625 Combine like terms: -0.2604166667 + 0.390625 = 0.1302083333 0.390625 + -1.25x + x2 = 0.1302083333 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.1302083333 Calculate the square root of the right side: 0.360843918 Break this problem into two subproblems by setting (x + -0.625) equal to 0.360843918 and -0.360843918.Subproblem 1
x + -0.625 = 0.360843918 Simplifying x + -0.625 = 0.360843918 Reorder the terms: -0.625 + x = 0.360843918 Solving -0.625 + x = 0.360843918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.360843918 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.360843918 + 0.625 x = 0.360843918 + 0.625 Combine like terms: 0.360843918 + 0.625 = 0.985843918 x = 0.985843918 Simplifying x = 0.985843918Subproblem 2
x + -0.625 = -0.360843918 Simplifying x + -0.625 = -0.360843918 Reorder the terms: -0.625 + x = -0.360843918 Solving -0.625 + x = -0.360843918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.360843918 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.360843918 + 0.625 x = -0.360843918 + 0.625 Combine like terms: -0.360843918 + 0.625 = 0.264156082 x = 0.264156082 Simplifying x = 0.264156082Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.985843918, 0.264156082}
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