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Simplifying 9x2 + 7x + -56 = 0 Reorder the terms: -56 + 7x + 9x2 = 0 Solving -56 + 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'. -6.222222222 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '6.222222222' to each side of the equation. -6.222222222 + 0.7777777778x + 6.222222222 + x2 = 0 + 6.222222222 Reorder the terms: -6.222222222 + 6.222222222 + 0.7777777778x + x2 = 0 + 6.222222222 Combine like terms: -6.222222222 + 6.222222222 = 0.000000000 0.000000000 + 0.7777777778x + x2 = 0 + 6.222222222 0.7777777778x + x2 = 0 + 6.222222222 Combine like terms: 0 + 6.222222222 = 6.222222222 0.7777777778x + x2 = 6.222222222 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 = 6.222222222 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 6.222222222 + 0.1512345679 Combine like terms: 6.222222222 + 0.1512345679 = 6.3734567899 0.1512345679 + 0.7777777778x + x2 = 6.3734567899 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 6.3734567899 Calculate the square root of the right side: 2.524570615 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 2.524570615 and -2.524570615.Subproblem 1
x + 0.3888888889 = 2.524570615 Simplifying x + 0.3888888889 = 2.524570615 Reorder the terms: 0.3888888889 + x = 2.524570615 Solving 0.3888888889 + x = 2.524570615 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 = 2.524570615 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 2.524570615 + -0.3888888889 x = 2.524570615 + -0.3888888889 Combine like terms: 2.524570615 + -0.3888888889 = 2.1356817261 x = 2.1356817261 Simplifying x = 2.1356817261Subproblem 2
x + 0.3888888889 = -2.524570615 Simplifying x + 0.3888888889 = -2.524570615 Reorder the terms: 0.3888888889 + x = -2.524570615 Solving 0.3888888889 + x = -2.524570615 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 = -2.524570615 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -2.524570615 + -0.3888888889 x = -2.524570615 + -0.3888888889 Combine like terms: -2.524570615 + -0.3888888889 = -2.9134595039 x = -2.9134595039 Simplifying x = -2.9134595039Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1356817261, -2.9134595039}
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