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Simplifying 2x2 + 29x + 92 = 0 Reorder the terms: 92 + 29x + 2x2 = 0 Solving 92 + 29x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 46 + 14.5x + x2 = 0 Move the constant term to the right: Add '-46' to each side of the equation. 46 + 14.5x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + 14.5x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 14.5x + x2 = 0 + -46 14.5x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 14.5x + x2 = -46 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = -46 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = -46 + 52.5625 Combine like terms: -46 + 52.5625 = 6.5625 52.5625 + 14.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + 7.25) equal to 2.561737691 and -2.561737691.Subproblem 1
x + 7.25 = 2.561737691 Simplifying x + 7.25 = 2.561737691 Reorder the terms: 7.25 + x = 2.561737691 Solving 7.25 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 2.561737691 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 2.561737691 + -7.25 x = 2.561737691 + -7.25 Combine like terms: 2.561737691 + -7.25 = -4.688262309 x = -4.688262309 Simplifying x = -4.688262309Subproblem 2
x + 7.25 = -2.561737691 Simplifying x + 7.25 = -2.561737691 Reorder the terms: 7.25 + x = -2.561737691 Solving 7.25 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -2.561737691 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -2.561737691 + -7.25 x = -2.561737691 + -7.25 Combine like terms: -2.561737691 + -7.25 = -9.811737691 x = -9.811737691 Simplifying x = -9.811737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.688262309, -9.811737691}
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