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Simplifying 9x2 + -43x + -130 = 0 Reorder the terms: -130 + -43x + 9x2 = 0 Solving -130 + -43x + 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'. -14.44444444 + -4.777777778x + x2 = 0 Move the constant term to the right: Add '14.44444444' to each side of the equation. -14.44444444 + -4.777777778x + 14.44444444 + x2 = 0 + 14.44444444 Reorder the terms: -14.44444444 + 14.44444444 + -4.777777778x + x2 = 0 + 14.44444444 Combine like terms: -14.44444444 + 14.44444444 = 0.00000000 0.00000000 + -4.777777778x + x2 = 0 + 14.44444444 -4.777777778x + x2 = 0 + 14.44444444 Combine like terms: 0 + 14.44444444 = 14.44444444 -4.777777778x + x2 = 14.44444444 The x term is -4.777777778x. Take half its coefficient (-2.388888889). Square it (5.706790124) and add it to both sides. Add '5.706790124' to each side of the equation. -4.777777778x + 5.706790124 + x2 = 14.44444444 + 5.706790124 Reorder the terms: 5.706790124 + -4.777777778x + x2 = 14.44444444 + 5.706790124 Combine like terms: 14.44444444 + 5.706790124 = 20.151234564 5.706790124 + -4.777777778x + x2 = 20.151234564 Factor a perfect square on the left side: (x + -2.388888889)(x + -2.388888889) = 20.151234564 Calculate the square root of the right side: 4.489012649 Break this problem into two subproblems by setting (x + -2.388888889) equal to 4.489012649 and -4.489012649.Subproblem 1
x + -2.388888889 = 4.489012649 Simplifying x + -2.388888889 = 4.489012649 Reorder the terms: -2.388888889 + x = 4.489012649 Solving -2.388888889 + x = 4.489012649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.388888889' to each side of the equation. -2.388888889 + 2.388888889 + x = 4.489012649 + 2.388888889 Combine like terms: -2.388888889 + 2.388888889 = 0.000000000 0.000000000 + x = 4.489012649 + 2.388888889 x = 4.489012649 + 2.388888889 Combine like terms: 4.489012649 + 2.388888889 = 6.877901538 x = 6.877901538 Simplifying x = 6.877901538Subproblem 2
x + -2.388888889 = -4.489012649 Simplifying x + -2.388888889 = -4.489012649 Reorder the terms: -2.388888889 + x = -4.489012649 Solving -2.388888889 + x = -4.489012649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.388888889' to each side of the equation. -2.388888889 + 2.388888889 + x = -4.489012649 + 2.388888889 Combine like terms: -2.388888889 + 2.388888889 = 0.000000000 0.000000000 + x = -4.489012649 + 2.388888889 x = -4.489012649 + 2.388888889 Combine like terms: -4.489012649 + 2.388888889 = -2.10012376 x = -2.10012376 Simplifying x = -2.10012376Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.877901538, -2.10012376}
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