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Simplifying 45x2 + -143x + -12 = 0 Reorder the terms: -12 + -143x + 45x2 = 0 Solving -12 + -143x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.2666666667 + -3.177777778x + x2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -3.177777778x + 0.2666666667 + x2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -3.177777778x + x2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -3.177777778x + x2 = 0 + 0.2666666667 -3.177777778x + x2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -3.177777778x + x2 = 0.2666666667 The x term is -3.177777778x. Take half its coefficient (-1.588888889). Square it (2.524567902) and add it to both sides. Add '2.524567902' to each side of the equation. -3.177777778x + 2.524567902 + x2 = 0.2666666667 + 2.524567902 Reorder the terms: 2.524567902 + -3.177777778x + x2 = 0.2666666667 + 2.524567902 Combine like terms: 0.2666666667 + 2.524567902 = 2.7912345687 2.524567902 + -3.177777778x + x2 = 2.7912345687 Factor a perfect square on the left side: (x + -1.588888889)(x + -1.588888889) = 2.7912345687 Calculate the square root of the right side: 1.670698826 Break this problem into two subproblems by setting (x + -1.588888889) equal to 1.670698826 and -1.670698826.Subproblem 1
x + -1.588888889 = 1.670698826 Simplifying x + -1.588888889 = 1.670698826 Reorder the terms: -1.588888889 + x = 1.670698826 Solving -1.588888889 + x = 1.670698826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.588888889' to each side of the equation. -1.588888889 + 1.588888889 + x = 1.670698826 + 1.588888889 Combine like terms: -1.588888889 + 1.588888889 = 0.000000000 0.000000000 + x = 1.670698826 + 1.588888889 x = 1.670698826 + 1.588888889 Combine like terms: 1.670698826 + 1.588888889 = 3.259587715 x = 3.259587715 Simplifying x = 3.259587715Subproblem 2
x + -1.588888889 = -1.670698826 Simplifying x + -1.588888889 = -1.670698826 Reorder the terms: -1.588888889 + x = -1.670698826 Solving -1.588888889 + x = -1.670698826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.588888889' to each side of the equation. -1.588888889 + 1.588888889 + x = -1.670698826 + 1.588888889 Combine like terms: -1.588888889 + 1.588888889 = 0.000000000 0.000000000 + x = -1.670698826 + 1.588888889 x = -1.670698826 + 1.588888889 Combine like terms: -1.670698826 + 1.588888889 = -0.081809937 x = -0.081809937 Simplifying x = -0.081809937Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.259587715, -0.081809937}
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