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Simplifying 12x2 + -25x + 8 = 0 Reorder the terms: 8 + -25x + 12x2 = 0 Solving 8 + -25x + 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'. 0.6666666667 + -2.083333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -2.083333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -2.083333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -2.083333333x + x2 = 0 + -0.6666666667 -2.083333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -2.083333333x + x2 = -0.6666666667 The x term is -2.083333333x. Take half its coefficient (-1.041666667). Square it (1.085069445) and add it to both sides. Add '1.085069445' to each side of the equation. -2.083333333x + 1.085069445 + x2 = -0.6666666667 + 1.085069445 Reorder the terms: 1.085069445 + -2.083333333x + x2 = -0.6666666667 + 1.085069445 Combine like terms: -0.6666666667 + 1.085069445 = 0.4184027783 1.085069445 + -2.083333333x + x2 = 0.4184027783 Factor a perfect square on the left side: (x + -1.041666667)(x + -1.041666667) = 0.4184027783 Calculate the square root of the right side: 0.646840613 Break this problem into two subproblems by setting (x + -1.041666667) equal to 0.646840613 and -0.646840613.Subproblem 1
x + -1.041666667 = 0.646840613 Simplifying x + -1.041666667 = 0.646840613 Reorder the terms: -1.041666667 + x = 0.646840613 Solving -1.041666667 + x = 0.646840613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = 0.646840613 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = 0.646840613 + 1.041666667 x = 0.646840613 + 1.041666667 Combine like terms: 0.646840613 + 1.041666667 = 1.68850728 x = 1.68850728 Simplifying x = 1.68850728Subproblem 2
x + -1.041666667 = -0.646840613 Simplifying x + -1.041666667 = -0.646840613 Reorder the terms: -1.041666667 + x = -0.646840613 Solving -1.041666667 + x = -0.646840613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.041666667' to each side of the equation. -1.041666667 + 1.041666667 + x = -0.646840613 + 1.041666667 Combine like terms: -1.041666667 + 1.041666667 = 0.000000000 0.000000000 + x = -0.646840613 + 1.041666667 x = -0.646840613 + 1.041666667 Combine like terms: -0.646840613 + 1.041666667 = 0.394826054 x = 0.394826054 Simplifying x = 0.394826054Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.68850728, 0.394826054}
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