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Simplifying 3x(x + 4) = 11x + 9 Reorder the terms: 3x(4 + x) = 11x + 9 (4 * 3x + x * 3x) = 11x + 9 (12x + 3x2) = 11x + 9 Reorder the terms: 12x + 3x2 = 9 + 11x Solving 12x + 3x2 = 9 + 11x Solving for variable 'x'. Reorder the terms: -9 + 12x + -11x + 3x2 = 9 + 11x + -9 + -11x Combine like terms: 12x + -11x = 1x -9 + 1x + 3x2 = 9 + 11x + -9 + -11x Reorder the terms: -9 + 1x + 3x2 = 9 + -9 + 11x + -11x Combine like terms: 9 + -9 = 0 -9 + 1x + 3x2 = 0 + 11x + -11x -9 + 1x + 3x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -9 + 1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.3333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.3333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.3333333333x + x2 = 0 + 3 0.3333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.3333333333x + x2 = 3 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 3 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 3 + 0.02777777779 Combine like terms: 3 + 0.02777777779 = 3.02777777779 0.02777777779 + 0.3333333333x + x2 = 3.02777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 3.02777777779 Calculate the square root of the right side: 1.740051085 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.740051085 and -1.740051085.Subproblem 1
x + 0.1666666667 = 1.740051085 Simplifying x + 0.1666666667 = 1.740051085 Reorder the terms: 0.1666666667 + x = 1.740051085 Solving 0.1666666667 + x = 1.740051085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 1.740051085 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.740051085 + -0.1666666667 x = 1.740051085 + -0.1666666667 Combine like terms: 1.740051085 + -0.1666666667 = 1.5733844183 x = 1.5733844183 Simplifying x = 1.5733844183Subproblem 2
x + 0.1666666667 = -1.740051085 Simplifying x + 0.1666666667 = -1.740051085 Reorder the terms: 0.1666666667 + x = -1.740051085 Solving 0.1666666667 + x = -1.740051085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -1.740051085 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.740051085 + -0.1666666667 x = -1.740051085 + -0.1666666667 Combine like terms: -1.740051085 + -0.1666666667 = -1.9067177517 x = -1.9067177517 Simplifying x = -1.9067177517Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5733844183, -1.9067177517}
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