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Simplifying 9x2 + 36x + 29 = 0 Reorder the terms: 29 + 36x + 9x2 = 0 Solving 29 + 36x + 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'. 3.222222222 + 4x + x2 = 0 Move the constant term to the right: Add '-3.222222222' to each side of the equation. 3.222222222 + 4x + -3.222222222 + x2 = 0 + -3.222222222 Reorder the terms: 3.222222222 + -3.222222222 + 4x + x2 = 0 + -3.222222222 Combine like terms: 3.222222222 + -3.222222222 = 0.000000000 0.000000000 + 4x + x2 = 0 + -3.222222222 4x + x2 = 0 + -3.222222222 Combine like terms: 0 + -3.222222222 = -3.222222222 4x + x2 = -3.222222222 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.222222222 + 4 Reorder the terms: 4 + 4x + x2 = -3.222222222 + 4 Combine like terms: -3.222222222 + 4 = 0.777777778 4 + 4x + x2 = 0.777777778 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.777777778 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (x + 2) equal to 0.881917104 and -0.881917104.Subproblem 1
x + 2 = 0.881917104 Simplifying x + 2 = 0.881917104 Reorder the terms: 2 + x = 0.881917104 Solving 2 + x = 0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.881917104 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.881917104 + -2 x = 0.881917104 + -2 Combine like terms: 0.881917104 + -2 = -1.118082896 x = -1.118082896 Simplifying x = -1.118082896Subproblem 2
x + 2 = -0.881917104 Simplifying x + 2 = -0.881917104 Reorder the terms: 2 + x = -0.881917104 Solving 2 + x = -0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.881917104 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.881917104 + -2 x = -0.881917104 + -2 Combine like terms: -0.881917104 + -2 = -2.881917104 x = -2.881917104 Simplifying x = -2.881917104Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.118082896, -2.881917104}
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