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Simplifying 0 = -12x2 + -45x + -54 Reorder the terms: 0 = -54 + -45x + -12x2 Solving 0 = -54 + -45x + -12x2 Solving for variable 'x'. Combine like terms: 0 + 54 = 54 54 + 45x + 12x2 = -54 + -45x + -12x2 + 54 + 45x + 12x2 Reorder the terms: 54 + 45x + 12x2 = -54 + 54 + -45x + 45x + -12x2 + 12x2 Combine like terms: -54 + 54 = 0 54 + 45x + 12x2 = 0 + -45x + 45x + -12x2 + 12x2 54 + 45x + 12x2 = -45x + 45x + -12x2 + 12x2 Combine like terms: -45x + 45x = 0 54 + 45x + 12x2 = 0 + -12x2 + 12x2 54 + 45x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 54 + 45x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(18 + 15x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(18 + 15x + 4x2)' equal to zero and attempt to solve: Simplifying 18 + 15x + 4x2 = 0 Solving 18 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.5 + 3.75x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 3.75x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 3.75x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 3.75x + x2 = 0 + -4.5 3.75x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 3.75x + x2 = -4.5 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = -4.5 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -4.5 + 3.515625 Combine like terms: -4.5 + 3.515625 = -0.984375 3.515625 + 3.75x + x2 = -0.984375 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = -0.984375 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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