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Simplifying 2x2 + 27x + -9.5 = 0 Reorder the terms: -9.5 + 27x + 2x2 = 0 Solving -9.5 + 27x + 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 + 13.5x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 13.5x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 13.5x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 13.5x + x2 = 0 + 4.75 13.5x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 13.5x + x2 = 4.75 The x term is 13.5x. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x + 45.5625 + x2 = 4.75 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 4.75 + 45.5625 Combine like terms: 4.75 + 45.5625 = 50.3125 45.5625 + 13.5x + x2 = 50.3125 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 50.3125 Calculate the square root of the right side: 7.09313048 Break this problem into two subproblems by setting (x + 6.75) equal to 7.09313048 and -7.09313048.Subproblem 1
x + 6.75 = 7.09313048 Simplifying x + 6.75 = 7.09313048 Reorder the terms: 6.75 + x = 7.09313048 Solving 6.75 + x = 7.09313048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 7.09313048 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 7.09313048 + -6.75 x = 7.09313048 + -6.75 Combine like terms: 7.09313048 + -6.75 = 0.34313048 x = 0.34313048 Simplifying x = 0.34313048Subproblem 2
x + 6.75 = -7.09313048 Simplifying x + 6.75 = -7.09313048 Reorder the terms: 6.75 + x = -7.09313048 Solving 6.75 + x = -7.09313048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -7.09313048 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -7.09313048 + -6.75 x = -7.09313048 + -6.75 Combine like terms: -7.09313048 + -6.75 = -13.84313048 x = -13.84313048 Simplifying x = -13.84313048Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34313048, -13.84313048}
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