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Simplifying 9x2 + -61x + -60 = 0 Reorder the terms: -60 + -61x + 9x2 = 0 Solving -60 + -61x + 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 + -6.777777778x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -6.777777778x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -6.777777778x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -6.777777778x + x2 = 0 + 6.666666667 -6.777777778x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -6.777777778x + x2 = 6.666666667 The x term is -6.777777778x. Take half its coefficient (-3.388888889). Square it (11.48456790) and add it to both sides. Add '11.48456790' to each side of the equation. -6.777777778x + 11.48456790 + x2 = 6.666666667 + 11.48456790 Reorder the terms: 11.48456790 + -6.777777778x + x2 = 6.666666667 + 11.48456790 Combine like terms: 6.666666667 + 11.48456790 = 18.151234567 11.48456790 + -6.777777778x + x2 = 18.151234567 Factor a perfect square on the left side: (x + -3.388888889)(x + -3.388888889) = 18.151234567 Calculate the square root of the right side: 4.260426571 Break this problem into two subproblems by setting (x + -3.388888889) equal to 4.260426571 and -4.260426571.Subproblem 1
x + -3.388888889 = 4.260426571 Simplifying x + -3.388888889 = 4.260426571 Reorder the terms: -3.388888889 + x = 4.260426571 Solving -3.388888889 + x = 4.260426571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.388888889' to each side of the equation. -3.388888889 + 3.388888889 + x = 4.260426571 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = 4.260426571 + 3.388888889 x = 4.260426571 + 3.388888889 Combine like terms: 4.260426571 + 3.388888889 = 7.64931546 x = 7.64931546 Simplifying x = 7.64931546Subproblem 2
x + -3.388888889 = -4.260426571 Simplifying x + -3.388888889 = -4.260426571 Reorder the terms: -3.388888889 + x = -4.260426571 Solving -3.388888889 + x = -4.260426571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.388888889' to each side of the equation. -3.388888889 + 3.388888889 + x = -4.260426571 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = -4.260426571 + 3.388888889 x = -4.260426571 + 3.388888889 Combine like terms: -4.260426571 + 3.388888889 = -0.871537682 x = -0.871537682 Simplifying x = -0.871537682Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.64931546, -0.871537682}
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