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Simplifying (6x + 6)(6x + 6) = 50 Reorder the terms: (6 + 6x)(6x + 6) = 50 Reorder the terms: (6 + 6x)(6 + 6x) = 50 Multiply (6 + 6x) * (6 + 6x) (6(6 + 6x) + 6x * (6 + 6x)) = 50 ((6 * 6 + 6x * 6) + 6x * (6 + 6x)) = 50 ((36 + 36x) + 6x * (6 + 6x)) = 50 (36 + 36x + (6 * 6x + 6x * 6x)) = 50 (36 + 36x + (36x + 36x2)) = 50 Combine like terms: 36x + 36x = 72x (36 + 72x + 36x2) = 50 Solving 36 + 72x + 36x2 = 50 Solving for variable 'x'. Reorder the terms: 36 + -50 + 72x + 36x2 = 50 + -50 Combine like terms: 36 + -50 = -14 -14 + 72x + 36x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -14 + 72x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 36x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 36x + 18x2)' equal to zero and attempt to solve: Simplifying -7 + 36x + 18x2 = 0 Solving -7 + 36x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3888888889 + 2x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + 2x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + 2x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.3888888889 2x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 2x + x2 = 0.3888888889 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.3888888889 + 1 Reorder the terms: 1 + 2x + x2 = 0.3888888889 + 1 Combine like terms: 0.3888888889 + 1 = 1.3888888889 1 + 2x + x2 = 1.3888888889 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.3888888889 Calculate the square root of the right side: 1.178511302 Break this problem into two subproblems by setting (x + 1) equal to 1.178511302 and -1.178511302.Subproblem 1
x + 1 = 1.178511302 Simplifying x + 1 = 1.178511302 Reorder the terms: 1 + x = 1.178511302 Solving 1 + x = 1.178511302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.178511302 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.178511302 + -1 x = 1.178511302 + -1 Combine like terms: 1.178511302 + -1 = 0.178511302 x = 0.178511302 Simplifying x = 0.178511302Subproblem 2
x + 1 = -1.178511302 Simplifying x + 1 = -1.178511302 Reorder the terms: 1 + x = -1.178511302 Solving 1 + x = -1.178511302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.178511302 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.178511302 + -1 x = -1.178511302 + -1 Combine like terms: -1.178511302 + -1 = -2.178511302 x = -2.178511302 Simplifying x = -2.178511302Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.178511302, -2.178511302}Solution
x = {0.178511302, -2.178511302}
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