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Simplifying 9x2 + 15x + 12 = 0 Reorder the terms: 12 + 15x + 9x2 = 0 Solving 12 + 15x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 5x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 5x + 3x2 = 0 Solving 4 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + -1.333333333 1.666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.666666667x + x2 = -1.333333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -1.333333333 + 0.6944444447 Combine like terms: -1.333333333 + 0.6944444447 = -0.6388888883 0.6944444447 + 1.666666667x + x2 = -0.6388888883 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = -0.6388888883 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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