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Simplifying 4x2 + 29x + 49 = 0 Reorder the terms: 49 + 29x + 4x2 = 0 Solving 49 + 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'. 12.25 + 7.25x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + 7.25x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + 7.25x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + 7.25x + x2 = 0 + -12.25 7.25x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 7.25x + x2 = -12.25 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 = -12.25 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = -12.25 + 13.140625 Combine like terms: -12.25 + 13.140625 = 0.890625 13.140625 + 7.25x + x2 = 0.890625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 3.625) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 3.625 = 0.943729304 Simplifying x + 3.625 = 0.943729304 Reorder the terms: 3.625 + x = 0.943729304 Solving 3.625 + x = 0.943729304 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 = 0.943729304 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 0.943729304 + -3.625 x = 0.943729304 + -3.625 Combine like terms: 0.943729304 + -3.625 = -2.681270696 x = -2.681270696 Simplifying x = -2.681270696Subproblem 2
x + 3.625 = -0.943729304 Simplifying x + 3.625 = -0.943729304 Reorder the terms: 3.625 + x = -0.943729304 Solving 3.625 + x = -0.943729304 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 = -0.943729304 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -0.943729304 + -3.625 x = -0.943729304 + -3.625 Combine like terms: -0.943729304 + -3.625 = -4.568729304 x = -4.568729304 Simplifying x = -4.568729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.681270696, -4.568729304}
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