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Simplifying 3x2 + -27x + -20 = 0 Reorder the terms: -20 + -27x + 3x2 = 0 Solving -20 + -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'. -6.666666667 + -9x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -9x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -9x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -9x + x2 = 0 + 6.666666667 -9x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -9x + x2 = 6.666666667 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 = 6.666666667 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 6.666666667 + 20.25 Combine like terms: 6.666666667 + 20.25 = 26.916666667 20.25 + -9x + x2 = 26.916666667 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 26.916666667 Calculate the square root of the right side: 5.188127472 Break this problem into two subproblems by setting (x + -4.5) equal to 5.188127472 and -5.188127472.Subproblem 1
x + -4.5 = 5.188127472 Simplifying x + -4.5 = 5.188127472 Reorder the terms: -4.5 + x = 5.188127472 Solving -4.5 + x = 5.188127472 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 = 5.188127472 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.188127472 + 4.5 x = 5.188127472 + 4.5 Combine like terms: 5.188127472 + 4.5 = 9.688127472 x = 9.688127472 Simplifying x = 9.688127472Subproblem 2
x + -4.5 = -5.188127472 Simplifying x + -4.5 = -5.188127472 Reorder the terms: -4.5 + x = -5.188127472 Solving -4.5 + x = -5.188127472 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 = -5.188127472 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.188127472 + 4.5 x = -5.188127472 + 4.5 Combine like terms: -5.188127472 + 4.5 = -0.688127472 x = -0.688127472 Simplifying x = -0.688127472Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.688127472, -0.688127472}
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