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Simplifying 12x2 + -72x + 77 = 0 Reorder the terms: 77 + -72x + 12x2 = 0 Solving 77 + -72x + 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'. 6.416666667 + -6x + x2 = 0 Move the constant term to the right: Add '-6.416666667' to each side of the equation. 6.416666667 + -6x + -6.416666667 + x2 = 0 + -6.416666667 Reorder the terms: 6.416666667 + -6.416666667 + -6x + x2 = 0 + -6.416666667 Combine like terms: 6.416666667 + -6.416666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + -6.416666667 -6x + x2 = 0 + -6.416666667 Combine like terms: 0 + -6.416666667 = -6.416666667 -6x + x2 = -6.416666667 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 = -6.416666667 + 9 Reorder the terms: 9 + -6x + x2 = -6.416666667 + 9 Combine like terms: -6.416666667 + 9 = 2.583333333 9 + -6x + x2 = 2.583333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (x + -3) equal to 1.607275127 and -1.607275127.Subproblem 1
x + -3 = 1.607275127 Simplifying x + -3 = 1.607275127 Reorder the terms: -3 + x = 1.607275127 Solving -3 + x = 1.607275127 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 = 1.607275127 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.607275127 + 3 x = 1.607275127 + 3 Combine like terms: 1.607275127 + 3 = 4.607275127 x = 4.607275127 Simplifying x = 4.607275127Subproblem 2
x + -3 = -1.607275127 Simplifying x + -3 = -1.607275127 Reorder the terms: -3 + x = -1.607275127 Solving -3 + x = -1.607275127 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 = -1.607275127 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.607275127 + 3 x = -1.607275127 + 3 Combine like terms: -1.607275127 + 3 = 1.392724873 x = 1.392724873 Simplifying x = 1.392724873Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.607275127, 1.392724873}
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