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Simplifying 4x2 + 27x + 39 = 0 Reorder the terms: 39 + 27x + 4x2 = 0 Solving 39 + 27x + 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'. 9.75 + 6.75x + x2 = 0 Move the constant term to the right: Add '-9.75' to each side of the equation. 9.75 + 6.75x + -9.75 + x2 = 0 + -9.75 Reorder the terms: 9.75 + -9.75 + 6.75x + x2 = 0 + -9.75 Combine like terms: 9.75 + -9.75 = 0.00 0.00 + 6.75x + x2 = 0 + -9.75 6.75x + x2 = 0 + -9.75 Combine like terms: 0 + -9.75 = -9.75 6.75x + x2 = -9.75 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = -9.75 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -9.75 + 11.390625 Combine like terms: -9.75 + 11.390625 = 1.640625 11.390625 + 6.75x + x2 = 1.640625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 3.375) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 3.375 = 1.280868846 Simplifying x + 3.375 = 1.280868846 Reorder the terms: 3.375 + x = 1.280868846 Solving 3.375 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 1.280868846 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 1.280868846 + -3.375 x = 1.280868846 + -3.375 Combine like terms: 1.280868846 + -3.375 = -2.094131154 x = -2.094131154 Simplifying x = -2.094131154Subproblem 2
x + 3.375 = -1.280868846 Simplifying x + 3.375 = -1.280868846 Reorder the terms: 3.375 + x = -1.280868846 Solving 3.375 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -1.280868846 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -1.280868846 + -3.375 x = -1.280868846 + -3.375 Combine like terms: -1.280868846 + -3.375 = -4.655868846 x = -4.655868846 Simplifying x = -4.655868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.094131154, -4.655868846}
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