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Simplifying 3(x + 13)(x + 13) = 54 Reorder the terms: 3(13 + x)(x + 13) = 54 Reorder the terms: 3(13 + x)(13 + x) = 54 Multiply (13 + x) * (13 + x) 3(13(13 + x) + x(13 + x)) = 54 3((13 * 13 + x * 13) + x(13 + x)) = 54 3((169 + 13x) + x(13 + x)) = 54 3(169 + 13x + (13 * x + x * x)) = 54 3(169 + 13x + (13x + x2)) = 54 Combine like terms: 13x + 13x = 26x 3(169 + 26x + x2) = 54 (169 * 3 + 26x * 3 + x2 * 3) = 54 (507 + 78x + 3x2) = 54 Solving 507 + 78x + 3x2 = 54 Solving for variable 'x'. Reorder the terms: 507 + -54 + 78x + 3x2 = 54 + -54 Combine like terms: 507 + -54 = 453 453 + 78x + 3x2 = 54 + -54 Combine like terms: 54 + -54 = 0 453 + 78x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(151 + 26x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(151 + 26x + x2)' equal to zero and attempt to solve: Simplifying 151 + 26x + x2 = 0 Solving 151 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-151' to each side of the equation. 151 + 26x + -151 + x2 = 0 + -151 Reorder the terms: 151 + -151 + 26x + x2 = 0 + -151 Combine like terms: 151 + -151 = 0 0 + 26x + x2 = 0 + -151 26x + x2 = 0 + -151 Combine like terms: 0 + -151 = -151 26x + x2 = -151 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -151 + 169 Reorder the terms: 169 + 26x + x2 = -151 + 169 Combine like terms: -151 + 169 = 18 169 + 26x + x2 = 18 Factor a perfect square on the left side: (x + 13)(x + 13) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 13) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 13 = 4.242640687 Simplifying x + 13 = 4.242640687 Reorder the terms: 13 + x = 4.242640687 Solving 13 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 4.242640687 + -13 Combine like terms: 13 + -13 = 0 0 + x = 4.242640687 + -13 x = 4.242640687 + -13 Combine like terms: 4.242640687 + -13 = -8.757359313 x = -8.757359313 Simplifying x = -8.757359313Subproblem 2
x + 13 = -4.242640687 Simplifying x + 13 = -4.242640687 Reorder the terms: 13 + x = -4.242640687 Solving 13 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -4.242640687 + -13 Combine like terms: 13 + -13 = 0 0 + x = -4.242640687 + -13 x = -4.242640687 + -13 Combine like terms: -4.242640687 + -13 = -17.242640687 x = -17.242640687 Simplifying x = -17.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.757359313, -17.242640687}Solution
x = {-8.757359313, -17.242640687}
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