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Simplifying 3x2 + 18x + 27 = 2 Reorder the terms: 27 + 18x + 3x2 = 2 Solving 27 + 18x + 3x2 = 2 Solving for variable 'x'. Reorder the terms: 27 + -2 + 18x + 3x2 = 2 + -2 Combine like terms: 27 + -2 = 25 25 + 18x + 3x2 = 2 + -2 Combine like terms: 2 + -2 = 0 25 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.333333333 + 6x + x2 = 0 Move the constant term to the right: Add '-8.333333333' to each side of the equation. 8.333333333 + 6x + -8.333333333 + x2 = 0 + -8.333333333 Reorder the terms: 8.333333333 + -8.333333333 + 6x + x2 = 0 + -8.333333333 Combine like terms: 8.333333333 + -8.333333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + -8.333333333 6x + x2 = 0 + -8.333333333 Combine like terms: 0 + -8.333333333 = -8.333333333 6x + x2 = -8.333333333 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -8.333333333 + 9 Reorder the terms: 9 + 6x + x2 = -8.333333333 + 9 Combine like terms: -8.333333333 + 9 = 0.666666667 9 + 6x + x2 = 0.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + 3) equal to 0.816496581 and -0.816496581.Subproblem 1
x + 3 = 0.816496581 Simplifying x + 3 = 0.816496581 Reorder the terms: 3 + x = 0.816496581 Solving 3 + x = 0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0.816496581 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.816496581 + -3 x = 0.816496581 + -3 Combine like terms: 0.816496581 + -3 = -2.183503419 x = -2.183503419 Simplifying x = -2.183503419Subproblem 2
x + 3 = -0.816496581 Simplifying x + 3 = -0.816496581 Reorder the terms: 3 + x = -0.816496581 Solving 3 + x = -0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -0.816496581 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.816496581 + -3 x = -0.816496581 + -3 Combine like terms: -0.816496581 + -3 = -3.816496581 x = -3.816496581 Simplifying x = -3.816496581Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.183503419, -3.816496581}
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