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Simplifying 4x2 + 36x + 1 = 0 Reorder the terms: 1 + 36x + 4x2 = 0 Solving 1 + 36x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 9x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 9x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 9x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 9x + x2 = 0 + -0.25 9x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 9x + x2 = -0.25 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -0.25 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -0.25 + 20.25 Combine like terms: -0.25 + 20.25 = 20 20.25 + 9x + x2 = 20 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 4.5) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 4.5 = 4.472135955 Simplifying x + 4.5 = 4.472135955 Reorder the terms: 4.5 + x = 4.472135955 Solving 4.5 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.472135955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.472135955 + -4.5 x = 4.472135955 + -4.5 Combine like terms: 4.472135955 + -4.5 = -0.027864045 x = -0.027864045 Simplifying x = -0.027864045Subproblem 2
x + 4.5 = -4.472135955 Simplifying x + 4.5 = -4.472135955 Reorder the terms: 4.5 + x = -4.472135955 Solving 4.5 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.472135955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.472135955 + -4.5 x = -4.472135955 + -4.5 Combine like terms: -4.472135955 + -4.5 = -8.972135955 x = -8.972135955 Simplifying x = -8.972135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.027864045, -8.972135955}
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