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Simplifying 0 = 12x2 + -10x + 108 Reorder the terms: 0 = 108 + -10x + 12x2 Solving 0 = 108 + -10x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -108 = -108 -108 + 10x + -12x2 = 108 + -10x + 12x2 + -108 + 10x + -12x2 Reorder the terms: -108 + 10x + -12x2 = 108 + -108 + -10x + 10x + 12x2 + -12x2 Combine like terms: 108 + -108 = 0 -108 + 10x + -12x2 = 0 + -10x + 10x + 12x2 + -12x2 -108 + 10x + -12x2 = -10x + 10x + 12x2 + -12x2 Combine like terms: -10x + 10x = 0 -108 + 10x + -12x2 = 0 + 12x2 + -12x2 -108 + 10x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -108 + 10x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + 5x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + 5x + -6x2)' equal to zero and attempt to solve: Simplifying -54 + 5x + -6x2 = 0 Solving -54 + 5x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 9 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -0.8333333333x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -0.8333333333x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -0.8333333333x + x2 = 0 + -9 -0.8333333333x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -0.8333333333x + x2 = -9 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = -9 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -9 + 0.1736111111 Combine like terms: -9 + 0.1736111111 = -8.8263888889 0.1736111111 + -0.8333333333x + x2 = -8.8263888889 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = -8.8263888889 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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