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Simplifying 9x2 + -79x + 136 = 0 Reorder the terms: 136 + -79x + 9x2 = 0 Solving 136 + -79x + 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'. 15.11111111 + -8.777777778x + x2 = 0 Move the constant term to the right: Add '-15.11111111' to each side of the equation. 15.11111111 + -8.777777778x + -15.11111111 + x2 = 0 + -15.11111111 Reorder the terms: 15.11111111 + -15.11111111 + -8.777777778x + x2 = 0 + -15.11111111 Combine like terms: 15.11111111 + -15.11111111 = 0.00000000 0.00000000 + -8.777777778x + x2 = 0 + -15.11111111 -8.777777778x + x2 = 0 + -15.11111111 Combine like terms: 0 + -15.11111111 = -15.11111111 -8.777777778x + x2 = -15.11111111 The x term is -8.777777778x. Take half its coefficient (-4.388888889). Square it (19.26234568) and add it to both sides. Add '19.26234568' to each side of the equation. -8.777777778x + 19.26234568 + x2 = -15.11111111 + 19.26234568 Reorder the terms: 19.26234568 + -8.777777778x + x2 = -15.11111111 + 19.26234568 Combine like terms: -15.11111111 + 19.26234568 = 4.15123457 19.26234568 + -8.777777778x + x2 = 4.15123457 Factor a perfect square on the left side: (x + -4.388888889)(x + -4.388888889) = 4.15123457 Calculate the square root of the right side: 2.03745787 Break this problem into two subproblems by setting (x + -4.388888889) equal to 2.03745787 and -2.03745787.Subproblem 1
x + -4.388888889 = 2.03745787 Simplifying x + -4.388888889 = 2.03745787 Reorder the terms: -4.388888889 + x = 2.03745787 Solving -4.388888889 + x = 2.03745787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.388888889' to each side of the equation. -4.388888889 + 4.388888889 + x = 2.03745787 + 4.388888889 Combine like terms: -4.388888889 + 4.388888889 = 0.000000000 0.000000000 + x = 2.03745787 + 4.388888889 x = 2.03745787 + 4.388888889 Combine like terms: 2.03745787 + 4.388888889 = 6.426346759 x = 6.426346759 Simplifying x = 6.426346759Subproblem 2
x + -4.388888889 = -2.03745787 Simplifying x + -4.388888889 = -2.03745787 Reorder the terms: -4.388888889 + x = -2.03745787 Solving -4.388888889 + x = -2.03745787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.388888889' to each side of the equation. -4.388888889 + 4.388888889 + x = -2.03745787 + 4.388888889 Combine like terms: -4.388888889 + 4.388888889 = 0.000000000 0.000000000 + x = -2.03745787 + 4.388888889 x = -2.03745787 + 4.388888889 Combine like terms: -2.03745787 + 4.388888889 = 2.351431019 x = 2.351431019 Simplifying x = 2.351431019Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.426346759, 2.351431019}
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