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Simplifying 21x2 + 54x + 132 = 0 Reorder the terms: 132 + 54x + 21x2 = 0 Solving 132 + 54x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(44 + 18x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(44 + 18x + 7x2)' equal to zero and attempt to solve: Simplifying 44 + 18x + 7x2 = 0 Solving 44 + 18x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 6.285714286 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '-6.285714286' to each side of the equation. 6.285714286 + 2.571428571x + -6.285714286 + x2 = 0 + -6.285714286 Reorder the terms: 6.285714286 + -6.285714286 + 2.571428571x + x2 = 0 + -6.285714286 Combine like terms: 6.285714286 + -6.285714286 = 0.000000000 0.000000000 + 2.571428571x + x2 = 0 + -6.285714286 2.571428571x + x2 = 0 + -6.285714286 Combine like terms: 0 + -6.285714286 = -6.285714286 2.571428571x + x2 = -6.285714286 The x term is 2.571428571x. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571x + 1.653061225 + x2 = -6.285714286 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = -6.285714286 + 1.653061225 Combine like terms: -6.285714286 + 1.653061225 = -4.632653061 1.653061225 + 2.571428571x + x2 = -4.632653061 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = -4.632653061 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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