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Simplifying 2x2 + 29x + -9.5 = 0 Reorder the terms: -9.5 + 29x + 2x2 = 0 Solving -9.5 + 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'. -4.75 + 14.5x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 14.5x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 14.5x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 14.5x + x2 = 0 + 4.75 14.5x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 14.5x + x2 = 4.75 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 = 4.75 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = 4.75 + 52.5625 Combine like terms: 4.75 + 52.5625 = 57.3125 52.5625 + 14.5x + x2 = 57.3125 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 57.3125 Calculate the square root of the right side: 7.570501965 Break this problem into two subproblems by setting (x + 7.25) equal to 7.570501965 and -7.570501965.Subproblem 1
x + 7.25 = 7.570501965 Simplifying x + 7.25 = 7.570501965 Reorder the terms: 7.25 + x = 7.570501965 Solving 7.25 + x = 7.570501965 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 = 7.570501965 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 7.570501965 + -7.25 x = 7.570501965 + -7.25 Combine like terms: 7.570501965 + -7.25 = 0.320501965 x = 0.320501965 Simplifying x = 0.320501965Subproblem 2
x + 7.25 = -7.570501965 Simplifying x + 7.25 = -7.570501965 Reorder the terms: 7.25 + x = -7.570501965 Solving 7.25 + x = -7.570501965 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 = -7.570501965 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -7.570501965 + -7.25 x = -7.570501965 + -7.25 Combine like terms: -7.570501965 + -7.25 = -14.820501965 x = -14.820501965 Simplifying x = -14.820501965Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.320501965, -14.820501965}
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