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Simplifying (12t2 + -5t + 12) + (17t + 2) = 0 Reorder the terms: (12 + -5t + 12t2) + (17t + 2) = 0 Remove parenthesis around (12 + -5t + 12t2) 12 + -5t + 12t2 + (17t + 2) = 0 Reorder the terms: 12 + -5t + 12t2 + (2 + 17t) = 0 Remove parenthesis around (2 + 17t) 12 + -5t + 12t2 + 2 + 17t = 0 Reorder the terms: 12 + 2 + -5t + 17t + 12t2 = 0 Combine like terms: 12 + 2 = 14 14 + -5t + 17t + 12t2 = 0 Combine like terms: -5t + 17t = 12t 14 + 12t + 12t2 = 0 Solving 14 + 12t + 12t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 6t + 6t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 6t + 6t2)' equal to zero and attempt to solve: Simplifying 7 + 6t + 6t2 = 0 Solving 7 + 6t + 6t2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + t + t2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + t + -1.166666667 + t2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + t + t2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + t + t2 = 0 + -1.166666667 t + t2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 t + t2 = -1.166666667 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = -1.166666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = -1.166666667 + 0.25 Combine like terms: -1.166666667 + 0.25 = -0.916666667 1.25 + t2 = -0.916666667 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -0.916666667 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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