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Simplifying 16t2 + 4t + 20 = 0 Reorder the terms: 20 + 4t + 16t2 = 0 Solving 20 + 4t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + t + 4t2)' equal to zero and attempt to solve: Simplifying 5 + t + 4t2 = 0 Solving 5 + t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.25t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.25t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.25t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.25t + t2 = 0 + -1.25 0.25t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.25t + t2 = -1.25 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25t + 0.25 + t2 = -1.25 + 0.25 Reorder the terms: 0.25 + 0.25t + t2 = -1.25 + 0.25 Combine like terms: -1.25 + 0.25 = -1 0.25 + 0.25t + t2 = -1 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -1 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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