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Simplifying 6x2 + -54x + 81 = 0 Reorder the terms: 81 + -54x + 6x2 = 0 Solving 81 + -54x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(27 + -18x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(27 + -18x + 2x2)' equal to zero and attempt to solve: Simplifying 27 + -18x + 2x2 = 0 Solving 27 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + -9x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -9x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -9x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -9x + x2 = 0 + -13.5 -9x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -9x + x2 = -13.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -13.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -13.5 + 20.25 Combine like terms: -13.5 + 20.25 = 6.75 20.25 + -9x + x2 = 6.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -4.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -4.5 = 2.598076211 Simplifying x + -4.5 = 2.598076211 Reorder the terms: -4.5 + x = 2.598076211 Solving -4.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.598076211 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.598076211 + 4.5 x = 2.598076211 + 4.5 Combine like terms: 2.598076211 + 4.5 = 7.098076211 x = 7.098076211 Simplifying x = 7.098076211Subproblem 2
x + -4.5 = -2.598076211 Simplifying x + -4.5 = -2.598076211 Reorder the terms: -4.5 + x = -2.598076211 Solving -4.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.598076211 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.598076211 + 4.5 x = -2.598076211 + 4.5 Combine like terms: -2.598076211 + 4.5 = 1.901923789 x = 1.901923789 Simplifying x = 1.901923789Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.098076211, 1.901923789}Solution
x = {7.098076211, 1.901923789}
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