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Simplifying 3(x2 + -12x + 36) = 9 Reorder the terms: 3(36 + -12x + x2) = 9 (36 * 3 + -12x * 3 + x2 * 3) = 9 (108 + -36x + 3x2) = 9 Solving 108 + -36x + 3x2 = 9 Solving for variable 'x'. Reorder the terms: 108 + -9 + -36x + 3x2 = 9 + -9 Combine like terms: 108 + -9 = 99 99 + -36x + 3x2 = 9 + -9 Combine like terms: 9 + -9 = 0 99 + -36x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(33 + -12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(33 + -12x + x2)' equal to zero and attempt to solve: Simplifying 33 + -12x + x2 = 0 Solving 33 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -12x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + -12x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -12x + x2 = 0 + -33 -12x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 -12x + x2 = -33 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 = -33 + 36 Reorder the terms: 36 + -12x + x2 = -33 + 36 Combine like terms: -33 + 36 = 3 36 + -12x + x2 = 3 Factor a perfect square on the left side: (x + -6)(x + -6) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -6) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -6 = 1.732050808 Simplifying x + -6 = 1.732050808 Reorder the terms: -6 + x = 1.732050808 Solving -6 + x = 1.732050808 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 = 1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + x = 1.732050808 + 6 x = 1.732050808 + 6 Combine like terms: 1.732050808 + 6 = 7.732050808 x = 7.732050808 Simplifying x = 7.732050808Subproblem 2
x + -6 = -1.732050808 Simplifying x + -6 = -1.732050808 Reorder the terms: -6 + x = -1.732050808 Solving -6 + x = -1.732050808 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 = -1.732050808 + 6 Combine like terms: -6 + 6 = 0 0 + x = -1.732050808 + 6 x = -1.732050808 + 6 Combine like terms: -1.732050808 + 6 = 4.267949192 x = 4.267949192 Simplifying x = 4.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.732050808, 4.267949192}Solution
x = {7.732050808, 4.267949192}
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