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Simplifying 3x2 + -36x + 108 = 60 Reorder the terms: 108 + -36x + 3x2 = 60 Solving 108 + -36x + 3x2 = 60 Solving for variable 'x'. Reorder the terms: 108 + -60 + -36x + 3x2 = 60 + -60 Combine like terms: 108 + -60 = 48 48 + -36x + 3x2 = 60 + -60 Combine like terms: 60 + -60 = 0 48 + -36x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(16 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(16 + -12x + x2)' equal to zero and attempt to solve: Simplifying 16 + -12x + x2 = 0 Solving 16 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -12x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -12x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -12x + x2 = 0 + -16 -12x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -12x + x2 = -16 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -16 + 36 Reorder the terms: 36 + -12x + x2 = -16 + 36 Combine like terms: -16 + 36 = 20 36 + -12x + x2 = 20 Factor a perfect square on the left side: (x + -6)(x + -6) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -6) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -6 = 4.472135955 Simplifying x + -6 = 4.472135955 Reorder the terms: -6 + x = 4.472135955 Solving -6 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.472135955 + 6 x = 4.472135955 + 6 Combine like terms: 4.472135955 + 6 = 10.472135955 x = 10.472135955 Simplifying x = 10.472135955Subproblem 2
x + -6 = -4.472135955 Simplifying x + -6 = -4.472135955 Reorder the terms: -6 + x = -4.472135955 Solving -6 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.472135955 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.472135955 + 6 x = -4.472135955 + 6 Combine like terms: -4.472135955 + 6 = 1.527864045 x = 1.527864045 Simplifying x = 1.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.472135955, 1.527864045}Solution
x = {10.472135955, 1.527864045}
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