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Simplifying 42x2 + 69x + 666 = 0 Reorder the terms: 666 + 69x + 42x2 = 0 Solving 666 + 69x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(222 + 23x + 14x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(222 + 23x + 14x2)' equal to zero and attempt to solve: Simplifying 222 + 23x + 14x2 = 0 Solving 222 + 23x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 15.85714286 + 1.642857143x + x2 = 0 Move the constant term to the right: Add '-15.85714286' to each side of the equation. 15.85714286 + 1.642857143x + -15.85714286 + x2 = 0 + -15.85714286 Reorder the terms: 15.85714286 + -15.85714286 + 1.642857143x + x2 = 0 + -15.85714286 Combine like terms: 15.85714286 + -15.85714286 = 0.00000000 0.00000000 + 1.642857143x + x2 = 0 + -15.85714286 1.642857143x + x2 = 0 + -15.85714286 Combine like terms: 0 + -15.85714286 = -15.85714286 1.642857143x + x2 = -15.85714286 The x term is 1.642857143x. Take half its coefficient (0.8214285715). Square it (0.6747448981) and add it to both sides. Add '0.6747448981' to each side of the equation. 1.642857143x + 0.6747448981 + x2 = -15.85714286 + 0.6747448981 Reorder the terms: 0.6747448981 + 1.642857143x + x2 = -15.85714286 + 0.6747448981 Combine like terms: -15.85714286 + 0.6747448981 = -15.1823979619 0.6747448981 + 1.642857143x + x2 = -15.1823979619 Factor a perfect square on the left side: (x + 0.8214285715)(x + 0.8214285715) = -15.1823979619 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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