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Simplifying 3x2 + 27x + 8 = 0 Reorder the terms: 8 + 27x + 3x2 = 0 Solving 8 + 27x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 9x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 9x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 9x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 9x + x2 = 0 + -2.666666667 9x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 9x + x2 = -2.666666667 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -2.666666667 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -2.666666667 + 20.25 Combine like terms: -2.666666667 + 20.25 = 17.583333333 20.25 + 9x + x2 = 17.583333333 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 17.583333333 Calculate the square root of the right side: 4.193248542 Break this problem into two subproblems by setting (x + 4.5) equal to 4.193248542 and -4.193248542.Subproblem 1
x + 4.5 = 4.193248542 Simplifying x + 4.5 = 4.193248542 Reorder the terms: 4.5 + x = 4.193248542 Solving 4.5 + x = 4.193248542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.193248542 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.193248542 + -4.5 x = 4.193248542 + -4.5 Combine like terms: 4.193248542 + -4.5 = -0.306751458 x = -0.306751458 Simplifying x = -0.306751458Subproblem 2
x + 4.5 = -4.193248542 Simplifying x + 4.5 = -4.193248542 Reorder the terms: 4.5 + x = -4.193248542 Solving 4.5 + x = -4.193248542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.193248542 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.193248542 + -4.5 x = -4.193248542 + -4.5 Combine like terms: -4.193248542 + -4.5 = -8.693248542 x = -8.693248542 Simplifying x = -8.693248542Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.306751458, -8.693248542}
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