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Simplifying 3x2 + -27x + 9 = 0 Reorder the terms: 9 + -27x + 3x2 = 0 Solving 9 + -27x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -9x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -9x + x2)' equal to zero and attempt to solve: Simplifying 3 + -9x + x2 = 0 Solving 3 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -9x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -9x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -9x + x2 = 0 + -3 -9x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -9x + x2 = -3 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 = -3 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -3 + 20.25 Combine like terms: -3 + 20.25 = 17.25 20.25 + -9x + x2 = 17.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -4.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -4.5 = 4.153311931 Simplifying x + -4.5 = 4.153311931 Reorder the terms: -4.5 + x = 4.153311931 Solving -4.5 + x = 4.153311931 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 = 4.153311931 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.153311931 + 4.5 x = 4.153311931 + 4.5 Combine like terms: 4.153311931 + 4.5 = 8.653311931 x = 8.653311931 Simplifying x = 8.653311931Subproblem 2
x + -4.5 = -4.153311931 Simplifying x + -4.5 = -4.153311931 Reorder the terms: -4.5 + x = -4.153311931 Solving -4.5 + x = -4.153311931 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 = -4.153311931 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.153311931 + 4.5 x = -4.153311931 + 4.5 Combine like terms: -4.153311931 + 4.5 = 0.346688069 x = 0.346688069 Simplifying x = 0.346688069Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.653311931, 0.346688069}Solution
x = {8.653311931, 0.346688069}
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