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Simplifying 2x(11x + 11) = 6(2x + 12) Reorder the terms: 2x(11 + 11x) = 6(2x + 12) (11 * 2x + 11x * 2x) = 6(2x + 12) (22x + 22x2) = 6(2x + 12) Reorder the terms: 22x + 22x2 = 6(12 + 2x) 22x + 22x2 = (12 * 6 + 2x * 6) 22x + 22x2 = (72 + 12x) Solving 22x + 22x2 = 72 + 12x Solving for variable 'x'. Reorder the terms: -72 + 22x + -12x + 22x2 = 72 + 12x + -72 + -12x Combine like terms: 22x + -12x = 10x -72 + 10x + 22x2 = 72 + 12x + -72 + -12x Reorder the terms: -72 + 10x + 22x2 = 72 + -72 + 12x + -12x Combine like terms: 72 + -72 = 0 -72 + 10x + 22x2 = 0 + 12x + -12x -72 + 10x + 22x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -72 + 10x + 22x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 5x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 5x + 11x2)' equal to zero and attempt to solve: Simplifying -36 + 5x + 11x2 = 0 Solving -36 + 5x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -3.272727273 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '3.272727273' to each side of the equation. -3.272727273 + 0.4545454545x + 3.272727273 + x2 = 0 + 3.272727273 Reorder the terms: -3.272727273 + 3.272727273 + 0.4545454545x + x2 = 0 + 3.272727273 Combine like terms: -3.272727273 + 3.272727273 = 0.000000000 0.000000000 + 0.4545454545x + x2 = 0 + 3.272727273 0.4545454545x + x2 = 0 + 3.272727273 Combine like terms: 0 + 3.272727273 = 3.272727273 0.4545454545x + x2 = 3.272727273 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 3.272727273 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 3.272727273 + 0.05165289257 Combine like terms: 3.272727273 + 0.05165289257 = 3.32438016557 0.05165289257 + 0.4545454545x + x2 = 3.32438016557 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 3.32438016557 Calculate the square root of the right side: 1.823288284 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 1.823288284 and -1.823288284.Subproblem 1
x + 0.2272727273 = 1.823288284 Simplifying x + 0.2272727273 = 1.823288284 Reorder the terms: 0.2272727273 + x = 1.823288284 Solving 0.2272727273 + x = 1.823288284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 1.823288284 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 1.823288284 + -0.2272727273 x = 1.823288284 + -0.2272727273 Combine like terms: 1.823288284 + -0.2272727273 = 1.5960155567 x = 1.5960155567 Simplifying x = 1.5960155567Subproblem 2
x + 0.2272727273 = -1.823288284 Simplifying x + 0.2272727273 = -1.823288284 Reorder the terms: 0.2272727273 + x = -1.823288284 Solving 0.2272727273 + x = -1.823288284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -1.823288284 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -1.823288284 + -0.2272727273 x = -1.823288284 + -0.2272727273 Combine like terms: -1.823288284 + -0.2272727273 = -2.0505610113 x = -2.0505610113 Simplifying x = -2.0505610113Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5960155567, -2.0505610113}Solution
x = {1.5960155567, -2.0505610113}
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