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Simplifying (t) = 16t2 + 16t + 4 t = 16t2 + 16t + 4 Reorder the terms: t = 4 + 16t + 16t2 Solving t = 4 + 16t + 16t2 Solving for variable 't'. Reorder the terms: -4 + t + -16t + -16t2 = 4 + 16t + 16t2 + -4 + -16t + -16t2 Combine like terms: t + -16t = -15t -4 + -15t + -16t2 = 4 + 16t + 16t2 + -4 + -16t + -16t2 Reorder the terms: -4 + -15t + -16t2 = 4 + -4 + 16t + -16t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -15t + -16t2 = 0 + 16t + -16t + 16t2 + -16t2 -4 + -15t + -16t2 = 16t + -16t + 16t2 + -16t2 Combine like terms: 16t + -16t = 0 -4 + -15t + -16t2 = 0 + 16t2 + -16t2 -4 + -15t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -15t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 15t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 15t + 16t2)' equal to zero and attempt to solve: Simplifying 4 + 15t + 16t2 = 0 Solving 4 + 15t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + 0.9375t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.9375t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.9375t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.9375t + t2 = 0 + -0.25 0.9375t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.9375t + t2 = -0.25 The t term is 0.9375t. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375t + 0.2197265625 + t2 = -0.25 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = -0.25 + 0.2197265625 Combine like terms: -0.25 + 0.2197265625 = -0.0302734375 0.2197265625 + 0.9375t + t2 = -0.0302734375 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = -0.0302734375 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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