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Simplifying 0 = 56 + 15t + 3t2 Solving 0 = 56 + 15t + 3t2 Solving for variable 't'. Combine like terms: 0 + -56 = -56 -56 + -15t + -3t2 = 56 + 15t + 3t2 + -56 + -15t + -3t2 Reorder the terms: -56 + -15t + -3t2 = 56 + -56 + 15t + -15t + 3t2 + -3t2 Combine like terms: 56 + -56 = 0 -56 + -15t + -3t2 = 0 + 15t + -15t + 3t2 + -3t2 -56 + -15t + -3t2 = 15t + -15t + 3t2 + -3t2 Combine like terms: 15t + -15t = 0 -56 + -15t + -3t2 = 0 + 3t2 + -3t2 -56 + -15t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 -56 + -15t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(56 + 15t + 3t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(56 + 15t + 3t2)' equal to zero and attempt to solve: Simplifying 56 + 15t + 3t2 = 0 Solving 56 + 15t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 18.66666667 + 5t + t2 = 0 Move the constant term to the right: Add '-18.66666667' to each side of the equation. 18.66666667 + 5t + -18.66666667 + t2 = 0 + -18.66666667 Reorder the terms: 18.66666667 + -18.66666667 + 5t + t2 = 0 + -18.66666667 Combine like terms: 18.66666667 + -18.66666667 = 0.00000000 0.00000000 + 5t + t2 = 0 + -18.66666667 5t + t2 = 0 + -18.66666667 Combine like terms: 0 + -18.66666667 = -18.66666667 5t + t2 = -18.66666667 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = -18.66666667 + 6.25 Reorder the terms: 6.25 + 5t + t2 = -18.66666667 + 6.25 Combine like terms: -18.66666667 + 6.25 = -12.41666667 6.25 + 5t + t2 = -12.41666667 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = -12.41666667 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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