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Simplifying 36 = 12t + -2t2 Solving 36 = 12t + -2t2 Solving for variable 't'. Reorder the terms: 36 + -12t + 2t2 = 12t + -12t + -2t2 + 2t2 Combine like terms: 12t + -12t = 0 36 + -12t + 2t2 = 0 + -2t2 + 2t2 36 + -12t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 36 + -12t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -6t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -6t + t2)' equal to zero and attempt to solve: Simplifying 18 + -6t + t2 = 0 Solving 18 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -6t + -18 + t2 = 0 + -18 Reorder the terms: 18 + -18 + -6t + t2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -6t + t2 = 0 + -18 -6t + t2 = 0 + -18 Combine like terms: 0 + -18 = -18 -6t + t2 = -18 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -18 + 9 Reorder the terms: 9 + -6t + t2 = -18 + 9 Combine like terms: -18 + 9 = -9 9 + -6t + t2 = -9 Factor a perfect square on the left side: (t + -3)(t + -3) = -9 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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