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Simplifying -9x2 + -7x + 19 = 0 Reorder the terms: 19 + -7x + -9x2 = 0 Solving 19 + -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'. -2.111111111 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '2.111111111' to each side of the equation. -2.111111111 + 0.7777777778x + 2.111111111 + x2 = 0 + 2.111111111 Reorder the terms: -2.111111111 + 2.111111111 + 0.7777777778x + x2 = 0 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + 0.7777777778x + x2 = 0 + 2.111111111 0.7777777778x + x2 = 0 + 2.111111111 Combine like terms: 0 + 2.111111111 = 2.111111111 0.7777777778x + x2 = 2.111111111 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 = 2.111111111 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 2.111111111 + 0.1512345679 Combine like terms: 2.111111111 + 0.1512345679 = 2.2623456789 0.1512345679 + 0.7777777778x + x2 = 2.2623456789 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 2.2623456789 Calculate the square root of the right side: 1.504109597 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 1.504109597 and -1.504109597.Subproblem 1
x + 0.3888888889 = 1.504109597 Simplifying x + 0.3888888889 = 1.504109597 Reorder the terms: 0.3888888889 + x = 1.504109597 Solving 0.3888888889 + x = 1.504109597 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 = 1.504109597 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 1.504109597 + -0.3888888889 x = 1.504109597 + -0.3888888889 Combine like terms: 1.504109597 + -0.3888888889 = 1.1152207081 x = 1.1152207081 Simplifying x = 1.1152207081Subproblem 2
x + 0.3888888889 = -1.504109597 Simplifying x + 0.3888888889 = -1.504109597 Reorder the terms: 0.3888888889 + x = -1.504109597 Solving 0.3888888889 + x = -1.504109597 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 = -1.504109597 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -1.504109597 + -0.3888888889 x = -1.504109597 + -0.3888888889 Combine like terms: -1.504109597 + -0.3888888889 = -1.8929984859 x = -1.8929984859 Simplifying x = -1.8929984859Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1152207081, -1.8929984859}
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