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Simplifying 9x2 + 29x + 2 = 0 Reorder the terms: 2 + 29x + 9x2 = 0 Solving 2 + 29x + 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'. 0.2222222222 + 3.222222222x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 3.222222222x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 3.222222222x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 3.222222222x + x2 = 0 + -0.2222222222 3.222222222x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 3.222222222x + x2 = -0.2222222222 The x term is 3.222222222x. Take half its coefficient (1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. 3.222222222x + 2.595679012 + x2 = -0.2222222222 + 2.595679012 Reorder the terms: 2.595679012 + 3.222222222x + x2 = -0.2222222222 + 2.595679012 Combine like terms: -0.2222222222 + 2.595679012 = 2.3734567898 2.595679012 + 3.222222222x + x2 = 2.3734567898 Factor a perfect square on the left side: (x + 1.611111111)(x + 1.611111111) = 2.3734567898 Calculate the square root of the right side: 1.540602736 Break this problem into two subproblems by setting (x + 1.611111111) equal to 1.540602736 and -1.540602736.Subproblem 1
x + 1.611111111 = 1.540602736 Simplifying x + 1.611111111 = 1.540602736 Reorder the terms: 1.611111111 + x = 1.540602736 Solving 1.611111111 + x = 1.540602736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = 1.540602736 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = 1.540602736 + -1.611111111 x = 1.540602736 + -1.611111111 Combine like terms: 1.540602736 + -1.611111111 = -0.070508375 x = -0.070508375 Simplifying x = -0.070508375Subproblem 2
x + 1.611111111 = -1.540602736 Simplifying x + 1.611111111 = -1.540602736 Reorder the terms: 1.611111111 + x = -1.540602736 Solving 1.611111111 + x = -1.540602736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = -1.540602736 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = -1.540602736 + -1.611111111 x = -1.540602736 + -1.611111111 Combine like terms: -1.540602736 + -1.611111111 = -3.151713847 x = -3.151713847 Simplifying x = -3.151713847Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.070508375, -3.151713847}
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