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Simplifying 9x2 + 7x + -30 = 0 Reorder the terms: -30 + 7x + 9x2 = 0 Solving -30 + 7x + 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 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 0.7777777778x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 0.7777777778x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 0.7777777778x + x2 = 0 + 3.333333333 0.7777777778x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 0.7777777778x + x2 = 3.333333333 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 3.333333333 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 3.333333333 + 0.1512345679 Combine like terms: 3.333333333 + 0.1512345679 = 3.4845679009 0.1512345679 + 0.7777777778x + x2 = 3.4845679009 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 3.4845679009 Calculate the square root of the right side: 1.866699735 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 1.866699735 and -1.866699735.Subproblem 1
x + 0.3888888889 = 1.866699735 Simplifying x + 0.3888888889 = 1.866699735 Reorder the terms: 0.3888888889 + x = 1.866699735 Solving 0.3888888889 + x = 1.866699735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 1.866699735 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 1.866699735 + -0.3888888889 x = 1.866699735 + -0.3888888889 Combine like terms: 1.866699735 + -0.3888888889 = 1.4778108461 x = 1.4778108461 Simplifying x = 1.4778108461Subproblem 2
x + 0.3888888889 = -1.866699735 Simplifying x + 0.3888888889 = -1.866699735 Reorder the terms: 0.3888888889 + x = -1.866699735 Solving 0.3888888889 + x = -1.866699735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -1.866699735 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -1.866699735 + -0.3888888889 x = -1.866699735 + -0.3888888889 Combine like terms: -1.866699735 + -0.3888888889 = -2.2555886239 x = -2.2555886239 Simplifying x = -2.2555886239Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4778108461, -2.2555886239}
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