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Simplifying 138x2 + -213x + 81 = 0 Reorder the terms: 81 + -213x + 138x2 = 0 Solving 81 + -213x + 138x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(27 + -71x + 46x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(27 + -71x + 46x2)' equal to zero and attempt to solve: Simplifying 27 + -71x + 46x2 = 0 Solving 27 + -71x + 46x2 = 0 Begin completing the square. Divide all terms by 46 the coefficient of the squared term: Divide each side by '46'. 0.5869565217 + -1.543478261x + x2 = 0 Move the constant term to the right: Add '-0.5869565217' to each side of the equation. 0.5869565217 + -1.543478261x + -0.5869565217 + x2 = 0 + -0.5869565217 Reorder the terms: 0.5869565217 + -0.5869565217 + -1.543478261x + x2 = 0 + -0.5869565217 Combine like terms: 0.5869565217 + -0.5869565217 = 0.0000000000 0.0000000000 + -1.543478261x + x2 = 0 + -0.5869565217 -1.543478261x + x2 = 0 + -0.5869565217 Combine like terms: 0 + -0.5869565217 = -0.5869565217 -1.543478261x + x2 = -0.5869565217 The x term is -1.543478261x. Take half its coefficient (-0.7717391305). Square it (0.5955812855) and add it to both sides. Add '0.5955812855' to each side of the equation. -1.543478261x + 0.5955812855 + x2 = -0.5869565217 + 0.5955812855 Reorder the terms: 0.5955812855 + -1.543478261x + x2 = -0.5869565217 + 0.5955812855 Combine like terms: -0.5869565217 + 0.5955812855 = 0.0086247638 0.5955812855 + -1.543478261x + x2 = 0.0086247638 Factor a perfect square on the left side: (x + -0.7717391305)(x + -0.7717391305) = 0.0086247638 Calculate the square root of the right side: 0.092869606 Break this problem into two subproblems by setting (x + -0.7717391305) equal to 0.092869606 and -0.092869606.Subproblem 1
x + -0.7717391305 = 0.092869606 Simplifying x + -0.7717391305 = 0.092869606 Reorder the terms: -0.7717391305 + x = 0.092869606 Solving -0.7717391305 + x = 0.092869606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7717391305' to each side of the equation. -0.7717391305 + 0.7717391305 + x = 0.092869606 + 0.7717391305 Combine like terms: -0.7717391305 + 0.7717391305 = 0.0000000000 0.0000000000 + x = 0.092869606 + 0.7717391305 x = 0.092869606 + 0.7717391305 Combine like terms: 0.092869606 + 0.7717391305 = 0.8646087365 x = 0.8646087365 Simplifying x = 0.8646087365Subproblem 2
x + -0.7717391305 = -0.092869606 Simplifying x + -0.7717391305 = -0.092869606 Reorder the terms: -0.7717391305 + x = -0.092869606 Solving -0.7717391305 + x = -0.092869606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7717391305' to each side of the equation. -0.7717391305 + 0.7717391305 + x = -0.092869606 + 0.7717391305 Combine like terms: -0.7717391305 + 0.7717391305 = 0.0000000000 0.0000000000 + x = -0.092869606 + 0.7717391305 x = -0.092869606 + 0.7717391305 Combine like terms: -0.092869606 + 0.7717391305 = 0.6788695245 x = 0.6788695245 Simplifying x = 0.6788695245Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8646087365, 0.6788695245}Solution
x = {0.8646087365, 0.6788695245}
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