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Simplifying 12x2 + -72x + 80 = 52.514 Reorder the terms: 80 + -72x + 12x2 = 52.514 Solving 80 + -72x + 12x2 = 52.514 Solving for variable 'x'. Reorder the terms: 80 + -52.514 + -72x + 12x2 = 52.514 + -52.514 Combine like terms: 80 + -52.514 = 27.486 27.486 + -72x + 12x2 = 52.514 + -52.514 Combine like terms: 52.514 + -52.514 = 0.000 27.486 + -72x + 12x2 = 0.000 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 2.2905 + -6x + x2 = 0.000 Move the constant term to the right: Add '-2.2905' to each side of the equation. 2.2905 + -6x + -2.2905 + x2 = 0.000 + -2.2905 Reorder the terms: 2.2905 + -2.2905 + -6x + x2 = 0.000 + -2.2905 Combine like terms: 2.2905 + -2.2905 = 0.0000 0.0000 + -6x + x2 = 0.000 + -2.2905 -6x + x2 = 0.000 + -2.2905 Combine like terms: 0.000 + -2.2905 = -2.2905 -6x + x2 = -2.2905 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -2.2905 + 9 Reorder the terms: 9 + -6x + x2 = -2.2905 + 9 Combine like terms: -2.2905 + 9 = 6.7095 9 + -6x + x2 = 6.7095 Factor a perfect square on the left side: (x + -3)(x + -3) = 6.7095 Calculate the square root of the right side: 2.590270256 Break this problem into two subproblems by setting (x + -3) equal to 2.590270256 and -2.590270256.Subproblem 1
x + -3 = 2.590270256 Simplifying x + -3 = 2.590270256 Reorder the terms: -3 + x = 2.590270256 Solving -3 + x = 2.590270256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.590270256 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.590270256 + 3 x = 2.590270256 + 3 Combine like terms: 2.590270256 + 3 = 5.590270256 x = 5.590270256 Simplifying x = 5.590270256Subproblem 2
x + -3 = -2.590270256 Simplifying x + -3 = -2.590270256 Reorder the terms: -3 + x = -2.590270256 Solving -3 + x = -2.590270256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.590270256 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.590270256 + 3 x = -2.590270256 + 3 Combine like terms: -2.590270256 + 3 = 0.409729744 x = 0.409729744 Simplifying x = 0.409729744Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.590270256, 0.409729744}
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