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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 = 6.398346656 x = 6.398346656 Simplifying x = 6.398346656Subproblem 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 = 0.351653344 x = 0.351653344 Simplifying x = 0.351653344Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.398346656, 0.351653344}
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