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Simplifying 2x2 + 9x + -108 = 0 Reorder the terms: -108 + 9x + 2x2 = 0 Solving -108 + 9x + 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'. -54 + 4.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 4.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 4.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 4.5x + x2 = 0 + 54 4.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 4.5x + x2 = 54 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 54 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 54 + 5.0625 Combine like terms: 54 + 5.0625 = 59.0625 5.0625 + 4.5x + x2 = 59.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 59.0625 Calculate the square root of the right side: 7.685213074 Break this problem into two subproblems by setting (x + 2.25) equal to 7.685213074 and -7.685213074.Subproblem 1
x + 2.25 = 7.685213074 Simplifying x + 2.25 = 7.685213074 Reorder the terms: 2.25 + x = 7.685213074 Solving 2.25 + x = 7.685213074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 7.685213074 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 7.685213074 + -2.25 x = 7.685213074 + -2.25 Combine like terms: 7.685213074 + -2.25 = 5.435213074 x = 5.435213074 Simplifying x = 5.435213074Subproblem 2
x + 2.25 = -7.685213074 Simplifying x + 2.25 = -7.685213074 Reorder the terms: 2.25 + x = -7.685213074 Solving 2.25 + x = -7.685213074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -7.685213074 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -7.685213074 + -2.25 x = -7.685213074 + -2.25 Combine like terms: -7.685213074 + -2.25 = -9.935213074 x = -9.935213074 Simplifying x = -9.935213074Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.435213074, -9.935213074}
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