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Simplifying 3x2 + -54x + 162 = 0 Reorder the terms: 162 + -54x + 3x2 = 0 Solving 162 + -54x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(54 + -18x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(54 + -18x + x2)' equal to zero and attempt to solve: Simplifying 54 + -18x + x2 = 0 Solving 54 + -18x + x2 = 0 Begin completing the square. 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 = 27 81 + -18x + x2 = 27 Factor a perfect square on the left side: (x + -9)(x + -9) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -9) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -9 = 5.196152423 Simplifying x + -9 = 5.196152423 Reorder the terms: -9 + x = 5.196152423 Solving -9 + x = 5.196152423 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 = 5.196152423 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.196152423 + 9 x = 5.196152423 + 9 Combine like terms: 5.196152423 + 9 = 14.196152423 x = 14.196152423 Simplifying x = 14.196152423Subproblem 2
x + -9 = -5.196152423 Simplifying x + -9 = -5.196152423 Reorder the terms: -9 + x = -5.196152423 Solving -9 + x = -5.196152423 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 = -5.196152423 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.196152423 + 9 x = -5.196152423 + 9 Combine like terms: -5.196152423 + 9 = 3.803847577 x = 3.803847577 Simplifying x = 3.803847577Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.196152423, 3.803847577}Solution
x = {14.196152423, 3.803847577}
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