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Simplifying 9x2 + -79x + -130 = 0 Reorder the terms: -130 + -79x + 9x2 = 0 Solving -130 + -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'. -14.44444444 + -8.777777778x + x2 = 0 Move the constant term to the right: Add '14.44444444' to each side of the equation. -14.44444444 + -8.777777778x + 14.44444444 + x2 = 0 + 14.44444444 Reorder the terms: -14.44444444 + 14.44444444 + -8.777777778x + x2 = 0 + 14.44444444 Combine like terms: -14.44444444 + 14.44444444 = 0.00000000 0.00000000 + -8.777777778x + x2 = 0 + 14.44444444 -8.777777778x + x2 = 0 + 14.44444444 Combine like terms: 0 + 14.44444444 = 14.44444444 -8.777777778x + x2 = 14.44444444 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 = 14.44444444 + 19.26234568 Reorder the terms: 19.26234568 + -8.777777778x + x2 = 14.44444444 + 19.26234568 Combine like terms: 14.44444444 + 19.26234568 = 33.70679012 19.26234568 + -8.777777778x + x2 = 33.70679012 Factor a perfect square on the left side: (x + -4.388888889)(x + -4.388888889) = 33.70679012 Calculate the square root of the right side: 5.805754914 Break this problem into two subproblems by setting (x + -4.388888889) equal to 5.805754914 and -5.805754914.Subproblem 1
x + -4.388888889 = 5.805754914 Simplifying x + -4.388888889 = 5.805754914 Reorder the terms: -4.388888889 + x = 5.805754914 Solving -4.388888889 + x = 5.805754914 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 = 5.805754914 + 4.388888889 Combine like terms: -4.388888889 + 4.388888889 = 0.000000000 0.000000000 + x = 5.805754914 + 4.388888889 x = 5.805754914 + 4.388888889 Combine like terms: 5.805754914 + 4.388888889 = 10.194643803 x = 10.194643803 Simplifying x = 10.194643803Subproblem 2
x + -4.388888889 = -5.805754914 Simplifying x + -4.388888889 = -5.805754914 Reorder the terms: -4.388888889 + x = -5.805754914 Solving -4.388888889 + x = -5.805754914 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 = -5.805754914 + 4.388888889 Combine like terms: -4.388888889 + 4.388888889 = 0.000000000 0.000000000 + x = -5.805754914 + 4.388888889 x = -5.805754914 + 4.388888889 Combine like terms: -5.805754914 + 4.388888889 = -1.416866025 x = -1.416866025 Simplifying x = -1.416866025Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.194643803, -1.416866025}
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