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Simplifying 0 = -16t + 36t2 + 130 Reorder the terms: 0 = 130 + -16t + 36t2 Solving 0 = 130 + -16t + 36t2 Solving for variable 't'. Combine like terms: 0 + -130 = -130 -130 + 16t + -36t2 = 130 + -16t + 36t2 + -130 + 16t + -36t2 Reorder the terms: -130 + 16t + -36t2 = 130 + -130 + -16t + 16t + 36t2 + -36t2 Combine like terms: 130 + -130 = 0 -130 + 16t + -36t2 = 0 + -16t + 16t + 36t2 + -36t2 -130 + 16t + -36t2 = -16t + 16t + 36t2 + -36t2 Combine like terms: -16t + 16t = 0 -130 + 16t + -36t2 = 0 + 36t2 + -36t2 -130 + 16t + -36t2 = 36t2 + -36t2 Combine like terms: 36t2 + -36t2 = 0 -130 + 16t + -36t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 8t + -18t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 8t + -18t2)' equal to zero and attempt to solve: Simplifying -65 + 8t + -18t2 = 0 Solving -65 + 8t + -18t2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 3.611111111 + -0.4444444444t + t2 = 0 Move the constant term to the right: Add '-3.611111111' to each side of the equation. 3.611111111 + -0.4444444444t + -3.611111111 + t2 = 0 + -3.611111111 Reorder the terms: 3.611111111 + -3.611111111 + -0.4444444444t + t2 = 0 + -3.611111111 Combine like terms: 3.611111111 + -3.611111111 = 0.000000000 0.000000000 + -0.4444444444t + t2 = 0 + -3.611111111 -0.4444444444t + t2 = 0 + -3.611111111 Combine like terms: 0 + -3.611111111 = -3.611111111 -0.4444444444t + t2 = -3.611111111 The t term is -0.4444444444t. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444t + 0.04938271604 + t2 = -3.611111111 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444t + t2 = -3.611111111 + 0.04938271604 Combine like terms: -3.611111111 + 0.04938271604 = -3.56172839496 0.04938271604 + -0.4444444444t + t2 = -3.56172839496 Factor a perfect square on the left side: (t + -0.2222222222)(t + -0.2222222222) = -3.56172839496 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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