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Simplifying 9x2 + 26x + 8 = 0 Reorder the terms: 8 + 26x + 9x2 = 0 Solving 8 + 26x + 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'. 0.8888888889 + 2.888888889x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 2.888888889x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 2.888888889x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 2.888888889x + x2 = 0 + -0.8888888889 2.888888889x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 2.888888889x + x2 = -0.8888888889 The x term is 2.888888889x. Take half its coefficient (1.444444445). Square it (2.086419755) and add it to both sides. Add '2.086419755' to each side of the equation. 2.888888889x + 2.086419755 + x2 = -0.8888888889 + 2.086419755 Reorder the terms: 2.086419755 + 2.888888889x + x2 = -0.8888888889 + 2.086419755 Combine like terms: -0.8888888889 + 2.086419755 = 1.1975308661 2.086419755 + 2.888888889x + x2 = 1.1975308661 Factor a perfect square on the left side: (x + 1.444444445)(x + 1.444444445) = 1.1975308661 Calculate the square root of the right side: 1.094317534 Break this problem into two subproblems by setting (x + 1.444444445) equal to 1.094317534 and -1.094317534.Subproblem 1
x + 1.444444445 = 1.094317534 Simplifying x + 1.444444445 = 1.094317534 Reorder the terms: 1.444444445 + x = 1.094317534 Solving 1.444444445 + x = 1.094317534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.444444445' to each side of the equation. 1.444444445 + -1.444444445 + x = 1.094317534 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = 1.094317534 + -1.444444445 x = 1.094317534 + -1.444444445 Combine like terms: 1.094317534 + -1.444444445 = -0.350126911 x = -0.350126911 Simplifying x = -0.350126911Subproblem 2
x + 1.444444445 = -1.094317534 Simplifying x + 1.444444445 = -1.094317534 Reorder the terms: 1.444444445 + x = -1.094317534 Solving 1.444444445 + x = -1.094317534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.444444445' to each side of the equation. 1.444444445 + -1.444444445 + x = -1.094317534 + -1.444444445 Combine like terms: 1.444444445 + -1.444444445 = 0.000000000 0.000000000 + x = -1.094317534 + -1.444444445 x = -1.094317534 + -1.444444445 Combine like terms: -1.094317534 + -1.444444445 = -2.538761979 x = -2.538761979 Simplifying x = -2.538761979Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.350126911, -2.538761979}
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