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Simplifying 12x2 + -60x + 7 = 0 Reorder the terms: 7 + -60x + 12x2 = 0 Solving 7 + -60x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + -5x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + -5x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + -5x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + -0.5833333333 -5x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 -5x + x2 = -0.5833333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.5833333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.5833333333 + 6.25 Combine like terms: -0.5833333333 + 6.25 = 5.6666666667 6.25 + -5x + x2 = 5.6666666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.6666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (x + -2.5) equal to 2.380476143 and -2.380476143.Subproblem 1
x + -2.5 = 2.380476143 Simplifying x + -2.5 = 2.380476143 Reorder the terms: -2.5 + x = 2.380476143 Solving -2.5 + x = 2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.380476143 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.380476143 + 2.5 x = 2.380476143 + 2.5 Combine like terms: 2.380476143 + 2.5 = 4.880476143 x = 4.880476143 Simplifying x = 4.880476143Subproblem 2
x + -2.5 = -2.380476143 Simplifying x + -2.5 = -2.380476143 Reorder the terms: -2.5 + x = -2.380476143 Solving -2.5 + x = -2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.380476143 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.380476143 + 2.5 x = -2.380476143 + 2.5 Combine like terms: -2.380476143 + 2.5 = 0.119523857 x = 0.119523857 Simplifying x = 0.119523857Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.880476143, 0.119523857}
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