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Simplifying 6x2 + -54x + 27 = 0 Reorder the terms: 27 + -54x + 6x2 = 0 Solving 27 + -54x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -18x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -18x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -18x + 2x2 = 0 Solving 9 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -9x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -9x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -9x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -9x + x2 = 0 + -4.5 -9x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -9x + x2 = -4.5 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 = -4.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -4.5 + 20.25 Combine like terms: -4.5 + 20.25 = 15.75 20.25 + -9x + x2 = 15.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (x + -4.5) equal to 3.968626967 and -3.968626967.Subproblem 1
x + -4.5 = 3.968626967 Simplifying x + -4.5 = 3.968626967 Reorder the terms: -4.5 + x = 3.968626967 Solving -4.5 + x = 3.968626967 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 = 3.968626967 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.968626967 + 4.5 x = 3.968626967 + 4.5 Combine like terms: 3.968626967 + 4.5 = 8.468626967 x = 8.468626967 Simplifying x = 8.468626967Subproblem 2
x + -4.5 = -3.968626967 Simplifying x + -4.5 = -3.968626967 Reorder the terms: -4.5 + x = -3.968626967 Solving -4.5 + x = -3.968626967 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 = -3.968626967 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.968626967 + 4.5 x = -3.968626967 + 4.5 Combine like terms: -3.968626967 + 4.5 = 0.531373033 x = 0.531373033 Simplifying x = 0.531373033Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.468626967, 0.531373033}Solution
x = {8.468626967, 0.531373033}
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