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Simplifying 9x2 + -16x + -6 = 4 Reorder the terms: -6 + -16x + 9x2 = 4 Solving -6 + -16x + 9x2 = 4 Solving for variable 'x'. Reorder the terms: -6 + -4 + -16x + 9x2 = 4 + -4 Combine like terms: -6 + -4 = -10 -10 + -16x + 9x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -10 + -16x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -1.777777778x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -1.777777778x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -1.777777778x + x2 = 0 + 1.111111111 -1.777777778x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -1.777777778x + x2 = 1.111111111 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 = 1.111111111 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 1.111111111 + 0.7901234570 Combine like terms: 1.111111111 + 0.7901234570 = 1.901234568 0.7901234570 + -1.777777778x + x2 = 1.901234568 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 1.901234568 Calculate the square root of the right side: 1.378852627 Break this problem into two subproblems by setting (x + -0.888888889) equal to 1.378852627 and -1.378852627.Subproblem 1
x + -0.888888889 = 1.378852627 Simplifying x + -0.888888889 = 1.378852627 Reorder the terms: -0.888888889 + x = 1.378852627 Solving -0.888888889 + x = 1.378852627 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 = 1.378852627 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 1.378852627 + 0.888888889 x = 1.378852627 + 0.888888889 Combine like terms: 1.378852627 + 0.888888889 = 2.267741516 x = 2.267741516 Simplifying x = 2.267741516Subproblem 2
x + -0.888888889 = -1.378852627 Simplifying x + -0.888888889 = -1.378852627 Reorder the terms: -0.888888889 + x = -1.378852627 Solving -0.888888889 + x = -1.378852627 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 = -1.378852627 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -1.378852627 + 0.888888889 x = -1.378852627 + 0.888888889 Combine like terms: -1.378852627 + 0.888888889 = -0.489963738 x = -0.489963738 Simplifying x = -0.489963738Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.267741516, -0.489963738}
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