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Simplifying 6x2 + 15x + 171 = 0 Reorder the terms: 171 + 15x + 6x2 = 0 Solving 171 + 15x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(57 + 5x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(57 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying 57 + 5x + 2x2 = 0 Solving 57 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 28.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '-28.5' to each side of the equation. 28.5 + 2.5x + -28.5 + x2 = 0 + -28.5 Reorder the terms: 28.5 + -28.5 + 2.5x + x2 = 0 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + 2.5x + x2 = 0 + -28.5 2.5x + x2 = 0 + -28.5 Combine like terms: 0 + -28.5 = -28.5 2.5x + x2 = -28.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -28.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -28.5 + 1.5625 Combine like terms: -28.5 + 1.5625 = -26.9375 1.5625 + 2.5x + x2 = -26.9375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -26.9375 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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