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Simplifying 21x2 + 45x + 54 = 0 Reorder the terms: 54 + 45x + 21x2 = 0 Solving 54 + 45x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(18 + 15x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(18 + 15x + 7x2)' equal to zero and attempt to solve: Simplifying 18 + 15x + 7x2 = 0 Solving 18 + 15x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.571428571 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + 2.142857143x + -2.571428571 + x2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + 2.142857143x + x2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + 2.142857143x + x2 = 0 + -2.571428571 2.142857143x + x2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 2.142857143x + x2 = -2.571428571 The x term is 2.142857143x. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143x + 1.147959185 + x2 = -2.571428571 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = -2.571428571 + 1.147959185 Combine like terms: -2.571428571 + 1.147959185 = -1.423469386 1.147959185 + 2.142857143x + x2 = -1.423469386 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = -1.423469386 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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