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Simplifying 9x2 + -16x + -30 = 0 Reorder the terms: -30 + -16x + 9x2 = 0 Solving -30 + -16x + 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'. -3.333333333 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -1.777777778x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -1.777777778x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -1.777777778x + x2 = 0 + 3.333333333 -1.777777778x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -1.777777778x + x2 = 3.333333333 The x term is -1.777777778x. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778x + 0.7901234570 + x2 = 3.333333333 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 3.333333333 + 0.7901234570 Combine like terms: 3.333333333 + 0.7901234570 = 4.12345679 0.7901234570 + -1.777777778x + x2 = 4.12345679 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 4.12345679 Calculate the square root of the right side: 2.030629654 Break this problem into two subproblems by setting (x + -0.888888889) equal to 2.030629654 and -2.030629654.Subproblem 1
x + -0.888888889 = 2.030629654 Simplifying x + -0.888888889 = 2.030629654 Reorder the terms: -0.888888889 + x = 2.030629654 Solving -0.888888889 + x = 2.030629654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = 2.030629654 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 2.030629654 + 0.888888889 x = 2.030629654 + 0.888888889 Combine like terms: 2.030629654 + 0.888888889 = 2.919518543 x = 2.919518543 Simplifying x = 2.919518543Subproblem 2
x + -0.888888889 = -2.030629654 Simplifying x + -0.888888889 = -2.030629654 Reorder the terms: -0.888888889 + x = -2.030629654 Solving -0.888888889 + x = -2.030629654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = -2.030629654 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -2.030629654 + 0.888888889 x = -2.030629654 + 0.888888889 Combine like terms: -2.030629654 + 0.888888889 = -1.141740765 x = -1.141740765 Simplifying x = -1.141740765Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.919518543, -1.141740765}
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