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Simplifying 36x2 + 69x + 36 = 0 Reorder the terms: 36 + 69x + 36x2 = 0 Solving 36 + 69x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 23x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + 23x + 12x2)' equal to zero and attempt to solve: Simplifying 12 + 23x + 12x2 = 0 Solving 12 + 23x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1 + 1.916666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.916666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.916666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.916666667x + x2 = 0 + -1 1.916666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.916666667x + x2 = -1 The x term is 1.916666667x. Take half its coefficient (0.9583333335). Square it (0.9184027781) and add it to both sides. Add '0.9184027781' to each side of the equation. 1.916666667x + 0.9184027781 + x2 = -1 + 0.9184027781 Reorder the terms: 0.9184027781 + 1.916666667x + x2 = -1 + 0.9184027781 Combine like terms: -1 + 0.9184027781 = -0.0815972219 0.9184027781 + 1.916666667x + x2 = -0.0815972219 Factor a perfect square on the left side: (x + 0.9583333335)(x + 0.9583333335) = -0.0815972219 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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