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Simplifying 9x2 + -25x + 6 = 0 Reorder the terms: 6 + -25x + 9x2 = 0 Solving 6 + -25x + 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'. 0.6666666667 + -2.777777778x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -2.777777778x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -2.777777778x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -2.777777778x + x2 = 0 + -0.6666666667 -2.777777778x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -2.777777778x + x2 = -0.6666666667 The x term is -2.777777778x. Take half its coefficient (-1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. -2.777777778x + 1.929012346 + x2 = -0.6666666667 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x + x2 = -0.6666666667 + 1.929012346 Combine like terms: -0.6666666667 + 1.929012346 = 1.2623456793 1.929012346 + -2.777777778x + x2 = 1.2623456793 Factor a perfect square on the left side: (x + -1.388888889)(x + -1.388888889) = 1.2623456793 Calculate the square root of the right side: 1.123541579 Break this problem into two subproblems by setting (x + -1.388888889) equal to 1.123541579 and -1.123541579.Subproblem 1
x + -1.388888889 = 1.123541579 Simplifying x + -1.388888889 = 1.123541579 Reorder the terms: -1.388888889 + x = 1.123541579 Solving -1.388888889 + x = 1.123541579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = 1.123541579 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 1.123541579 + 1.388888889 x = 1.123541579 + 1.388888889 Combine like terms: 1.123541579 + 1.388888889 = 2.512430468 x = 2.512430468 Simplifying x = 2.512430468Subproblem 2
x + -1.388888889 = -1.123541579 Simplifying x + -1.388888889 = -1.123541579 Reorder the terms: -1.388888889 + x = -1.123541579 Solving -1.388888889 + x = -1.123541579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = -1.123541579 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -1.123541579 + 1.388888889 x = -1.123541579 + 1.388888889 Combine like terms: -1.123541579 + 1.388888889 = 0.26534731 x = 0.26534731 Simplifying x = 0.26534731Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.512430468, 0.26534731}
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