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Simplifying 16t2 + 84t + 112 = 0 Reorder the terms: 112 + 84t + 16t2 = 0 Solving 112 + 84t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(28 + 21t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(28 + 21t + 4t2)' equal to zero and attempt to solve: Simplifying 28 + 21t + 4t2 = 0 Solving 28 + 21t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7 + 5.25t + t2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 5.25t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + 5.25t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5.25t + t2 = 0 + -7 5.25t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 5.25t + t2 = -7 The t term is 5.25t. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25t + 6.890625 + t2 = -7 + 6.890625 Reorder the terms: 6.890625 + 5.25t + t2 = -7 + 6.890625 Combine like terms: -7 + 6.890625 = -0.109375 6.890625 + 5.25t + t2 = -0.109375 Factor a perfect square on the left side: (t + 2.625)(t + 2.625) = -0.109375 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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