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Simplifying 4x2 + 9x + -27 = 0 Reorder the terms: -27 + 9x + 4x2 = 0 Solving -27 + 9x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + 2.25x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 2.25x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 2.25x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 2.25x + x2 = 0 + 6.75 2.25x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 2.25x + x2 = 6.75 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 6.75 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 6.75 + 1.265625 Combine like terms: 6.75 + 1.265625 = 8.015625 1.265625 + 2.25x + x2 = 8.015625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 8.015625 Calculate the square root of the right side: 2.831187913 Break this problem into two subproblems by setting (x + 1.125) equal to 2.831187913 and -2.831187913.Subproblem 1
x + 1.125 = 2.831187913 Simplifying x + 1.125 = 2.831187913 Reorder the terms: 1.125 + x = 2.831187913 Solving 1.125 + x = 2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 2.831187913 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.831187913 + -1.125 x = 2.831187913 + -1.125 Combine like terms: 2.831187913 + -1.125 = 1.706187913 x = 1.706187913 Simplifying x = 1.706187913Subproblem 2
x + 1.125 = -2.831187913 Simplifying x + 1.125 = -2.831187913 Reorder the terms: 1.125 + x = -2.831187913 Solving 1.125 + x = -2.831187913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -2.831187913 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.831187913 + -1.125 x = -2.831187913 + -1.125 Combine like terms: -2.831187913 + -1.125 = -3.956187913 x = -3.956187913 Simplifying x = -3.956187913Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.706187913, -3.956187913}
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