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Simplifying 12x2 + 21x + 30 = 0 Reorder the terms: 30 + 21x + 12x2 = 0 Solving 30 + 21x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 7x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying 10 + 7x + 4x2 = 0 Solving 10 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 1.75x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 1.75x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 1.75x + x2 = 0 + -2.5 1.75x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 1.75x + x2 = -2.5 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -2.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -2.5 + 0.765625 Combine like terms: -2.5 + 0.765625 = -1.734375 0.765625 + 1.75x + x2 = -1.734375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -1.734375 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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