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Simplifying 12x2 + -60x + 73 = 0 Reorder the terms: 73 + -60x + 12x2 = 0 Solving 73 + -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'. 6.083333333 + -5x + x2 = 0 Move the constant term to the right: Add '-6.083333333' to each side of the equation. 6.083333333 + -5x + -6.083333333 + x2 = 0 + -6.083333333 Reorder the terms: 6.083333333 + -6.083333333 + -5x + x2 = 0 + -6.083333333 Combine like terms: 6.083333333 + -6.083333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + -6.083333333 -5x + x2 = 0 + -6.083333333 Combine like terms: 0 + -6.083333333 = -6.083333333 -5x + x2 = -6.083333333 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 = -6.083333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -6.083333333 + 6.25 Combine like terms: -6.083333333 + 6.25 = 0.166666667 6.25 + -5x + x2 = 0.166666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 0.166666667 Calculate the square root of the right side: 0.408248291 Break this problem into two subproblems by setting (x + -2.5) equal to 0.408248291 and -0.408248291.Subproblem 1
x + -2.5 = 0.408248291 Simplifying x + -2.5 = 0.408248291 Reorder the terms: -2.5 + x = 0.408248291 Solving -2.5 + x = 0.408248291 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 = 0.408248291 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 0.408248291 + 2.5 x = 0.408248291 + 2.5 Combine like terms: 0.408248291 + 2.5 = 2.908248291 x = 2.908248291 Simplifying x = 2.908248291Subproblem 2
x + -2.5 = -0.408248291 Simplifying x + -2.5 = -0.408248291 Reorder the terms: -2.5 + x = -0.408248291 Solving -2.5 + x = -0.408248291 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 = -0.408248291 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -0.408248291 + 2.5 x = -0.408248291 + 2.5 Combine like terms: -0.408248291 + 2.5 = 2.091751709 x = 2.091751709 Simplifying x = 2.091751709Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.908248291, 2.091751709}
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