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Simplifying x2 + -3x2 + -36x + 108 = 0 Reorder the terms: 108 + -36x + x2 + -3x2 = 0 Combine like terms: x2 + -3x2 = -2x2 108 + -36x + -2x2 = 0 Solving 108 + -36x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(54 + -18x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(54 + -18x + -1x2)' equal to zero and attempt to solve: Simplifying 54 + -18x + -1x2 = 0 Solving 54 + -18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + 18x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 18x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 18x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 18x + x2 = 0 + 54 18x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 18x + x2 = 54 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 54 + 81 Reorder the terms: 81 + 18x + x2 = 54 + 81 Combine like terms: 54 + 81 = 135 81 + 18x + x2 = 135 Factor a perfect square on the left side: (x + 9)(x + 9) = 135 Calculate the square root of the right side: 11.618950039 Break this problem into two subproblems by setting (x + 9) equal to 11.618950039 and -11.618950039.Subproblem 1
x + 9 = 11.618950039 Simplifying x + 9 = 11.618950039 Reorder the terms: 9 + x = 11.618950039 Solving 9 + x = 11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 11.618950039 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.618950039 + -9 x = 11.618950039 + -9 Combine like terms: 11.618950039 + -9 = 2.618950039 x = 2.618950039 Simplifying x = 2.618950039Subproblem 2
x + 9 = -11.618950039 Simplifying x + 9 = -11.618950039 Reorder the terms: 9 + x = -11.618950039 Solving 9 + x = -11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -11.618950039 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.618950039 + -9 x = -11.618950039 + -9 Combine like terms: -11.618950039 + -9 = -20.618950039 x = -20.618950039 Simplifying x = -20.618950039Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.618950039, -20.618950039}Solution
x = {2.618950039, -20.618950039}
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