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Simplifying 2x2 + 3x2 + -18x = 27 Reorder the terms: -18x + 2x2 + 3x2 = 27 Combine like terms: 2x2 + 3x2 = 5x2 -18x + 5x2 = 27 Solving -18x + 5x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -18x + 5x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + -3.6x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -3.6x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -3.6x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -3.6x + x2 = 0 + 5.4 -3.6x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -3.6x + x2 = 5.4 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 5.4 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 5.4 + 3.24 Combine like terms: 5.4 + 3.24 = 8.64 3.24 + -3.6x + x2 = 8.64 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 8.64 Calculate the square root of the right side: 2.939387691 Break this problem into two subproblems by setting (x + -1.8) equal to 2.939387691 and -2.939387691.Subproblem 1
x + -1.8 = 2.939387691 Simplifying x + -1.8 = 2.939387691 Reorder the terms: -1.8 + x = 2.939387691 Solving -1.8 + x = 2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 2.939387691 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.939387691 + 1.8 x = 2.939387691 + 1.8 Combine like terms: 2.939387691 + 1.8 = 4.739387691 x = 4.739387691 Simplifying x = 4.739387691Subproblem 2
x + -1.8 = -2.939387691 Simplifying x + -1.8 = -2.939387691 Reorder the terms: -1.8 + x = -2.939387691 Solving -1.8 + x = -2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -2.939387691 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.939387691 + 1.8 x = -2.939387691 + 1.8 Combine like terms: -2.939387691 + 1.8 = -1.139387691 x = -1.139387691 Simplifying x = -1.139387691Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.739387691, -1.139387691}
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