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Simplifying 9x2 + 79x + -28 = 0 Reorder the terms: -28 + 79x + 9x2 = 0 Solving -28 + 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'. -3.111111111 + 8.777777778x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + 8.777777778x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + 8.777777778x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + 8.777777778x + x2 = 0 + 3.111111111 8.777777778x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 8.777777778x + x2 = 3.111111111 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 = 3.111111111 + 19.26234568 Reorder the terms: 19.26234568 + 8.777777778x + x2 = 3.111111111 + 19.26234568 Combine like terms: 3.111111111 + 19.26234568 = 22.373456791 19.26234568 + 8.777777778x + x2 = 22.373456791 Factor a perfect square on the left side: (x + 4.388888889)(x + 4.388888889) = 22.373456791 Calculate the square root of the right side: 4.730058857 Break this problem into two subproblems by setting (x + 4.388888889) equal to 4.730058857 and -4.730058857.Subproblem 1
x + 4.388888889 = 4.730058857 Simplifying x + 4.388888889 = 4.730058857 Reorder the terms: 4.388888889 + x = 4.730058857 Solving 4.388888889 + x = 4.730058857 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 = 4.730058857 + -4.388888889 Combine like terms: 4.388888889 + -4.388888889 = 0.000000000 0.000000000 + x = 4.730058857 + -4.388888889 x = 4.730058857 + -4.388888889 Combine like terms: 4.730058857 + -4.388888889 = 0.341169968 x = 0.341169968 Simplifying x = 0.341169968Subproblem 2
x + 4.388888889 = -4.730058857 Simplifying x + 4.388888889 = -4.730058857 Reorder the terms: 4.388888889 + x = -4.730058857 Solving 4.388888889 + x = -4.730058857 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 = -4.730058857 + -4.388888889 Combine like terms: 4.388888889 + -4.388888889 = 0.000000000 0.000000000 + x = -4.730058857 + -4.388888889 x = -4.730058857 + -4.388888889 Combine like terms: -4.730058857 + -4.388888889 = -9.118947746 x = -9.118947746 Simplifying x = -9.118947746Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.341169968, -9.118947746}
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