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Simplifying 16t2 + 32t + 300 = 0 Reorder the terms: 300 + 32t + 16t2 = 0 Solving 300 + 32t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(75 + 8t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(75 + 8t + 4t2)' equal to zero and attempt to solve: Simplifying 75 + 8t + 4t2 = 0 Solving 75 + 8t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 18.75 + 2t + t2 = 0 Move the constant term to the right: Add '-18.75' to each side of the equation. 18.75 + 2t + -18.75 + t2 = 0 + -18.75 Reorder the terms: 18.75 + -18.75 + 2t + t2 = 0 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + 2t + t2 = 0 + -18.75 2t + t2 = 0 + -18.75 Combine like terms: 0 + -18.75 = -18.75 2t + t2 = -18.75 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = -18.75 + 1 Reorder the terms: 1 + 2t + t2 = -18.75 + 1 Combine like terms: -18.75 + 1 = -17.75 1 + 2t + t2 = -17.75 Factor a perfect square on the left side: (t + 1)(t + 1) = -17.75 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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