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Simplifying 2x2 + 27x + 64 = 0 Reorder the terms: 64 + 27x + 2x2 = 0 Solving 64 + 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'. 32 + 13.5x + x2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + 13.5x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 13.5x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 13.5x + x2 = 0 + -32 13.5x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 13.5x + x2 = -32 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 = -32 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = -32 + 45.5625 Combine like terms: -32 + 45.5625 = 13.5625 45.5625 + 13.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 6.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 6.75 = 3.682729966 Simplifying x + 6.75 = 3.682729966 Reorder the terms: 6.75 + x = 3.682729966 Solving 6.75 + x = 3.682729966 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 = 3.682729966 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 3.682729966 + -6.75 x = 3.682729966 + -6.75 Combine like terms: 3.682729966 + -6.75 = -3.067270034 x = -3.067270034 Simplifying x = -3.067270034Subproblem 2
x + 6.75 = -3.682729966 Simplifying x + 6.75 = -3.682729966 Reorder the terms: 6.75 + x = -3.682729966 Solving 6.75 + x = -3.682729966 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 = -3.682729966 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -3.682729966 + -6.75 x = -3.682729966 + -6.75 Combine like terms: -3.682729966 + -6.75 = -10.432729966 x = -10.432729966 Simplifying x = -10.432729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.067270034, -10.432729966}
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