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Simplifying 2x2 + -27x + 18 = 0 Reorder the terms: 18 + -27x + 2x2 = 0 Solving 18 + -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'. 9 + -13.5x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -13.5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -13.5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -13.5x + x2 = 0 + -9 -13.5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -13.5x + x2 = -9 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 = -9 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -9 + 45.5625 Combine like terms: -9 + 45.5625 = 36.5625 45.5625 + -13.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + -6.75) equal to 6.046693311 and -6.046693311.Subproblem 1
x + -6.75 = 6.046693311 Simplifying x + -6.75 = 6.046693311 Reorder the terms: -6.75 + x = 6.046693311 Solving -6.75 + x = 6.046693311 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 = 6.046693311 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 6.046693311 + 6.75 x = 6.046693311 + 6.75 Combine like terms: 6.046693311 + 6.75 = 12.796693311 x = 12.796693311 Simplifying x = 12.796693311Subproblem 2
x + -6.75 = -6.046693311 Simplifying x + -6.75 = -6.046693311 Reorder the terms: -6.75 + x = -6.046693311 Solving -6.75 + x = -6.046693311 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 = -6.046693311 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -6.046693311 + 6.75 x = -6.046693311 + 6.75 Combine like terms: -6.046693311 + 6.75 = 0.703306689 x = 0.703306689 Simplifying x = 0.703306689Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.796693311, 0.703306689}
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