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Simplifying 2x2 + -6x + -9 = 0 Reorder the terms: -9 + -6x + 2x2 = 0 Solving -9 + -6x + 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'. -4.5 + -3x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -3x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -3x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -3x + x2 = 0 + 4.5 -3x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -3x + x2 = 4.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 4.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 4.5 + 2.25 Combine like terms: 4.5 + 2.25 = 6.75 2.25 + -3x + x2 = 6.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -1.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -1.5 = 2.598076211 Simplifying x + -1.5 = 2.598076211 Reorder the terms: -1.5 + x = 2.598076211 Solving -1.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.598076211 + 1.5 x = 2.598076211 + 1.5 Combine like terms: 2.598076211 + 1.5 = 4.098076211 x = 4.098076211 Simplifying x = 4.098076211Subproblem 2
x + -1.5 = -2.598076211 Simplifying x + -1.5 = -2.598076211 Reorder the terms: -1.5 + x = -2.598076211 Solving -1.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.598076211 + 1.5 x = -2.598076211 + 1.5 Combine like terms: -2.598076211 + 1.5 = -1.098076211 x = -1.098076211 Simplifying x = -1.098076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.098076211, -1.098076211}
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