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Simplifying 4x2 + 29x + 4 + 5 = 0 Reorder the terms: 4 + 5 + 29x + 4x2 = 0 Combine like terms: 4 + 5 = 9 9 + 29x + 4x2 = 0 Solving 9 + 29x + 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'. 2.25 + 7.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 7.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 7.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 7.25x + x2 = 0 + -2.25 7.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 7.25x + x2 = -2.25 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = -2.25 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = -2.25 + 13.140625 Combine like terms: -2.25 + 13.140625 = 10.890625 13.140625 + 7.25x + x2 = 10.890625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting (x + 3.625) equal to 3.300094696 and -3.300094696.Subproblem 1
x + 3.625 = 3.300094696 Simplifying x + 3.625 = 3.300094696 Reorder the terms: 3.625 + x = 3.300094696 Solving 3.625 + x = 3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 3.300094696 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 3.300094696 + -3.625 x = 3.300094696 + -3.625 Combine like terms: 3.300094696 + -3.625 = -0.324905304 x = -0.324905304 Simplifying x = -0.324905304Subproblem 2
x + 3.625 = -3.300094696 Simplifying x + 3.625 = -3.300094696 Reorder the terms: 3.625 + x = -3.300094696 Solving 3.625 + x = -3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -3.300094696 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -3.300094696 + -3.625 x = -3.300094696 + -3.625 Combine like terms: -3.300094696 + -3.625 = -6.925094696 x = -6.925094696 Simplifying x = -6.925094696Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.324905304, -6.925094696}
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