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Simplifying 4x2 + 27x + 9 = 0 Reorder the terms: 9 + 27x + 4x2 = 0 Solving 9 + 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'. 2.25 + 6.75x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 6.75x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 6.75x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 6.75x + x2 = 0 + -2.25 6.75x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 6.75x + x2 = -2.25 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 = -2.25 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -2.25 + 11.390625 Combine like terms: -2.25 + 11.390625 = 9.140625 11.390625 + 6.75x + x2 = 9.140625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 9.140625 Calculate the square root of the right side: 3.023346656 Break this problem into two subproblems by setting (x + 3.375) equal to 3.023346656 and -3.023346656.Subproblem 1
x + 3.375 = 3.023346656 Simplifying x + 3.375 = 3.023346656 Reorder the terms: 3.375 + x = 3.023346656 Solving 3.375 + x = 3.023346656 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 = 3.023346656 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 3.023346656 + -3.375 x = 3.023346656 + -3.375 Combine like terms: 3.023346656 + -3.375 = -0.351653344 x = -0.351653344 Simplifying x = -0.351653344Subproblem 2
x + 3.375 = -3.023346656 Simplifying x + 3.375 = -3.023346656 Reorder the terms: 3.375 + x = -3.023346656 Solving 3.375 + x = -3.023346656 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 = -3.023346656 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -3.023346656 + -3.375 x = -3.023346656 + -3.375 Combine like terms: -3.023346656 + -3.375 = -6.398346656 x = -6.398346656 Simplifying x = -6.398346656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.351653344, -6.398346656}
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