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Simplifying 11x(4x + 16) = 78 Reorder the terms: 11x(16 + 4x) = 78 (16 * 11x + 4x * 11x) = 78 (176x + 44x2) = 78 Solving 176x + 44x2 = 78 Solving for variable 'x'. Reorder the terms: -78 + 176x + 44x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -78 + 176x + 44x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-39 + 88x + 22x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-39 + 88x + 22x2)' equal to zero and attempt to solve: Simplifying -39 + 88x + 22x2 = 0 Solving -39 + 88x + 22x2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -1.772727273 + 4x + x2 = 0 Move the constant term to the right: Add '1.772727273' to each side of the equation. -1.772727273 + 4x + 1.772727273 + x2 = 0 + 1.772727273 Reorder the terms: -1.772727273 + 1.772727273 + 4x + x2 = 0 + 1.772727273 Combine like terms: -1.772727273 + 1.772727273 = 0.000000000 0.000000000 + 4x + x2 = 0 + 1.772727273 4x + x2 = 0 + 1.772727273 Combine like terms: 0 + 1.772727273 = 1.772727273 4x + x2 = 1.772727273 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.772727273 + 4 Reorder the terms: 4 + 4x + x2 = 1.772727273 + 4 Combine like terms: 1.772727273 + 4 = 5.772727273 4 + 4x + x2 = 5.772727273 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.772727273 Calculate the square root of the right side: 2.402650052 Break this problem into two subproblems by setting (x + 2) equal to 2.402650052 and -2.402650052.Subproblem 1
x + 2 = 2.402650052 Simplifying x + 2 = 2.402650052 Reorder the terms: 2 + x = 2.402650052 Solving 2 + x = 2.402650052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.402650052 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.402650052 + -2 x = 2.402650052 + -2 Combine like terms: 2.402650052 + -2 = 0.402650052 x = 0.402650052 Simplifying x = 0.402650052Subproblem 2
x + 2 = -2.402650052 Simplifying x + 2 = -2.402650052 Reorder the terms: 2 + x = -2.402650052 Solving 2 + x = -2.402650052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.402650052 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.402650052 + -2 x = -2.402650052 + -2 Combine like terms: -2.402650052 + -2 = -4.402650052 x = -4.402650052 Simplifying x = -4.402650052Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.402650052, -4.402650052}Solution
x = {0.402650052, -4.402650052}
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