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Simplifying 36x2 + -363x + 144 = 0 Reorder the terms: 144 + -363x + 36x2 = 0 Solving 144 + -363x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(48 + -121x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(48 + -121x + 12x2)' equal to zero and attempt to solve: Simplifying 48 + -121x + 12x2 = 0 Solving 48 + -121x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 4 + -10.08333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10.08333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -10.08333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10.08333333x + x2 = 0 + -4 -10.08333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10.08333333x + x2 = -4 The x term is -10.08333333x. Take half its coefficient (-5.041666665). Square it (25.41840276) and add it to both sides. Add '25.41840276' to each side of the equation. -10.08333333x + 25.41840276 + x2 = -4 + 25.41840276 Reorder the terms: 25.41840276 + -10.08333333x + x2 = -4 + 25.41840276 Combine like terms: -4 + 25.41840276 = 21.41840276 25.41840276 + -10.08333333x + x2 = 21.41840276 Factor a perfect square on the left side: (x + -5.041666665)(x + -5.041666665) = 21.41840276 Calculate the square root of the right side: 4.628002027 Break this problem into two subproblems by setting (x + -5.041666665) equal to 4.628002027 and -4.628002027.Subproblem 1
x + -5.041666665 = 4.628002027 Simplifying x + -5.041666665 = 4.628002027 Reorder the terms: -5.041666665 + x = 4.628002027 Solving -5.041666665 + x = 4.628002027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.041666665' to each side of the equation. -5.041666665 + 5.041666665 + x = 4.628002027 + 5.041666665 Combine like terms: -5.041666665 + 5.041666665 = 0.000000000 0.000000000 + x = 4.628002027 + 5.041666665 x = 4.628002027 + 5.041666665 Combine like terms: 4.628002027 + 5.041666665 = 9.669668692 x = 9.669668692 Simplifying x = 9.669668692Subproblem 2
x + -5.041666665 = -4.628002027 Simplifying x + -5.041666665 = -4.628002027 Reorder the terms: -5.041666665 + x = -4.628002027 Solving -5.041666665 + x = -4.628002027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.041666665' to each side of the equation. -5.041666665 + 5.041666665 + x = -4.628002027 + 5.041666665 Combine like terms: -5.041666665 + 5.041666665 = 0.000000000 0.000000000 + x = -4.628002027 + 5.041666665 x = -4.628002027 + 5.041666665 Combine like terms: -4.628002027 + 5.041666665 = 0.413664638 x = 0.413664638 Simplifying x = 0.413664638Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.669668692, 0.413664638}Solution
x = {9.669668692, 0.413664638}
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