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Simplifying 9x2 + -31x + -60 = 0 Reorder the terms: -60 + -31x + 9x2 = 0 Solving -60 + -31x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.666666667 + -3.444444444x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -3.444444444x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -3.444444444x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -3.444444444x + x2 = 0 + 6.666666667 -3.444444444x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -3.444444444x + x2 = 6.666666667 The x term is -3.444444444x. Take half its coefficient (-1.722222222). Square it (2.966049382) and add it to both sides. Add '2.966049382' to each side of the equation. -3.444444444x + 2.966049382 + x2 = 6.666666667 + 2.966049382 Reorder the terms: 2.966049382 + -3.444444444x + x2 = 6.666666667 + 2.966049382 Combine like terms: 6.666666667 + 2.966049382 = 9.632716049 2.966049382 + -3.444444444x + x2 = 9.632716049 Factor a perfect square on the left side: (x + -1.722222222)(x + -1.722222222) = 9.632716049 Calculate the square root of the right side: 3.103661716 Break this problem into two subproblems by setting (x + -1.722222222) equal to 3.103661716 and -3.103661716.Subproblem 1
x + -1.722222222 = 3.103661716 Simplifying x + -1.722222222 = 3.103661716 Reorder the terms: -1.722222222 + x = 3.103661716 Solving -1.722222222 + x = 3.103661716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = 3.103661716 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = 3.103661716 + 1.722222222 x = 3.103661716 + 1.722222222 Combine like terms: 3.103661716 + 1.722222222 = 4.825883938 x = 4.825883938 Simplifying x = 4.825883938Subproblem 2
x + -1.722222222 = -3.103661716 Simplifying x + -1.722222222 = -3.103661716 Reorder the terms: -1.722222222 + x = -3.103661716 Solving -1.722222222 + x = -3.103661716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = -3.103661716 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = -3.103661716 + 1.722222222 x = -3.103661716 + 1.722222222 Combine like terms: -3.103661716 + 1.722222222 = -1.381439494 x = -1.381439494 Simplifying x = -1.381439494Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.825883938, -1.381439494}
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