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Simplifying 3x2 + -54x + 9 = 0 Reorder the terms: 9 + -54x + 3x2 = 0 Solving 9 + -54x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -18x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -18x + x2)' equal to zero and attempt to solve: Simplifying 3 + -18x + x2 = 0 Solving 3 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -18x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -18x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -18x + x2 = 0 + -3 -18x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -18x + x2 = -3 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 = -3 + 81 Reorder the terms: 81 + -18x + x2 = -3 + 81 Combine like terms: -3 + 81 = 78 81 + -18x + x2 = 78 Factor a perfect square on the left side: (x + -9)(x + -9) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + -9) equal to 8.831760866 and -8.831760866.Subproblem 1
x + -9 = 8.831760866 Simplifying x + -9 = 8.831760866 Reorder the terms: -9 + x = 8.831760866 Solving -9 + x = 8.831760866 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 = 8.831760866 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.831760866 + 9 x = 8.831760866 + 9 Combine like terms: 8.831760866 + 9 = 17.831760866 x = 17.831760866 Simplifying x = 17.831760866Subproblem 2
x + -9 = -8.831760866 Simplifying x + -9 = -8.831760866 Reorder the terms: -9 + x = -8.831760866 Solving -9 + x = -8.831760866 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 = -8.831760866 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.831760866 + 9 x = -8.831760866 + 9 Combine like terms: -8.831760866 + 9 = 0.168239134 x = 0.168239134 Simplifying x = 0.168239134Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.831760866, 0.168239134}Solution
x = {17.831760866, 0.168239134}
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