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Simplifying 3x2 + -60 = -6x2 + -7x + -40 Reorder the terms: -60 + 3x2 = -6x2 + -7x + -40 Reorder the terms: -60 + 3x2 = -40 + -7x + -6x2 Solving -60 + 3x2 = -40 + -7x + -6x2 Solving for variable 'x'. Reorder the terms: -60 + 40 + 7x + 3x2 + 6x2 = -40 + -7x + -6x2 + 40 + 7x + 6x2 Combine like terms: -60 + 40 = -20 -20 + 7x + 3x2 + 6x2 = -40 + -7x + -6x2 + 40 + 7x + 6x2 Combine like terms: 3x2 + 6x2 = 9x2 -20 + 7x + 9x2 = -40 + -7x + -6x2 + 40 + 7x + 6x2 Reorder the terms: -20 + 7x + 9x2 = -40 + 40 + -7x + 7x + -6x2 + 6x2 Combine like terms: -40 + 40 = 0 -20 + 7x + 9x2 = 0 + -7x + 7x + -6x2 + 6x2 -20 + 7x + 9x2 = -7x + 7x + -6x2 + 6x2 Combine like terms: -7x + 7x = 0 -20 + 7x + 9x2 = 0 + -6x2 + 6x2 -20 + 7x + 9x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -20 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 0.7777777778x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 0.7777777778x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 0.7777777778x + x2 = 0 + 2.222222222 0.7777777778x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 0.7777777778x + x2 = 2.222222222 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 2.222222222 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 2.222222222 + 0.1512345679 Combine like terms: 2.222222222 + 0.1512345679 = 2.3734567899 0.1512345679 + 0.7777777778x + x2 = 2.3734567899 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 2.3734567899 Calculate the square root of the right side: 1.540602736 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 1.540602736 and -1.540602736.Subproblem 1
x + 0.3888888889 = 1.540602736 Simplifying x + 0.3888888889 = 1.540602736 Reorder the terms: 0.3888888889 + x = 1.540602736 Solving 0.3888888889 + x = 1.540602736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 1.540602736 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 1.540602736 + -0.3888888889 x = 1.540602736 + -0.3888888889 Combine like terms: 1.540602736 + -0.3888888889 = 1.1517138471 x = 1.1517138471 Simplifying x = 1.1517138471Subproblem 2
x + 0.3888888889 = -1.540602736 Simplifying x + 0.3888888889 = -1.540602736 Reorder the terms: 0.3888888889 + x = -1.540602736 Solving 0.3888888889 + x = -1.540602736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -1.540602736 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -1.540602736 + -0.3888888889 x = -1.540602736 + -0.3888888889 Combine like terms: -1.540602736 + -0.3888888889 = -1.9294916249 x = -1.9294916249 Simplifying x = -1.9294916249Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1517138471, -1.9294916249}
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