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Simplifying 5x2 + 30x + 27 = 0 Reorder the terms: 27 + 30x + 5x2 = 0 Solving 27 + 30x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.4 + 6x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + 6x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + 6x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + 6x + x2 = 0 + -5.4 6x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 6x + x2 = -5.4 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 = -5.4 + 9 Reorder the terms: 9 + 6x + x2 = -5.4 + 9 Combine like terms: -5.4 + 9 = 3.6 9 + 6x + x2 = 3.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (x + 3) equal to 1.897366596 and -1.897366596.Subproblem 1
x + 3 = 1.897366596 Simplifying x + 3 = 1.897366596 Reorder the terms: 3 + x = 1.897366596 Solving 3 + x = 1.897366596 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 = 1.897366596 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.897366596 + -3 x = 1.897366596 + -3 Combine like terms: 1.897366596 + -3 = -1.102633404 x = -1.102633404 Simplifying x = -1.102633404Subproblem 2
x + 3 = -1.897366596 Simplifying x + 3 = -1.897366596 Reorder the terms: 3 + x = -1.897366596 Solving 3 + x = -1.897366596 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 = -1.897366596 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.897366596 + -3 x = -1.897366596 + -3 Combine like terms: -1.897366596 + -3 = -4.897366596 x = -4.897366596 Simplifying x = -4.897366596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.102633404, -4.897366596}
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