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Simplifying 3x2 + -18x + 9 = 11 Reorder the terms: 9 + -18x + 3x2 = 11 Solving 9 + -18x + 3x2 = 11 Solving for variable 'x'. Reorder the terms: 9 + -11 + -18x + 3x2 = 11 + -11 Combine like terms: 9 + -11 = -2 -2 + -18x + 3x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -2 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -6x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -6x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -6x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + 0.6666666667 -6x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -6x + x2 = 0.6666666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.6666666667 + 9 Reorder the terms: 9 + -6x + x2 = 0.6666666667 + 9 Combine like terms: 0.6666666667 + 9 = 9.6666666667 9 + -6x + x2 = 9.6666666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.6666666667 Calculate the square root of the right side: 3.109126351 Break this problem into two subproblems by setting (x + -3) equal to 3.109126351 and -3.109126351.Subproblem 1
x + -3 = 3.109126351 Simplifying x + -3 = 3.109126351 Reorder the terms: -3 + x = 3.109126351 Solving -3 + x = 3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.109126351 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.109126351 + 3 x = 3.109126351 + 3 Combine like terms: 3.109126351 + 3 = 6.109126351 x = 6.109126351 Simplifying x = 6.109126351Subproblem 2
x + -3 = -3.109126351 Simplifying x + -3 = -3.109126351 Reorder the terms: -3 + x = -3.109126351 Solving -3 + x = -3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.109126351 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.109126351 + 3 x = -3.109126351 + 3 Combine like terms: -3.109126351 + 3 = -0.109126351 x = -0.109126351 Simplifying x = -0.109126351Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.109126351, -0.109126351}
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