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Simplifying 0 = 16t2 + 8t + 15 Reorder the terms: 0 = 15 + 8t + 16t2 Solving 0 = 15 + 8t + 16t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -8t + -16t2 = 15 + 8t + 16t2 + -15 + -8t + -16t2 Reorder the terms: -15 + -8t + -16t2 = 15 + -15 + 8t + -8t + 16t2 + -16t2 Combine like terms: 15 + -15 = 0 -15 + -8t + -16t2 = 0 + 8t + -8t + 16t2 + -16t2 -15 + -8t + -16t2 = 8t + -8t + 16t2 + -16t2 Combine like terms: 8t + -8t = 0 -15 + -8t + -16t2 = 0 + 16t2 + -16t2 -15 + -8t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -15 + -8t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 8t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 8t + 16t2)' equal to zero and attempt to solve: Simplifying 15 + 8t + 16t2 = 0 Solving 15 + 8t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.9375 + 0.5t + t2 = 0 Move the constant term to the right: Add '-0.9375' to each side of the equation. 0.9375 + 0.5t + -0.9375 + t2 = 0 + -0.9375 Reorder the terms: 0.9375 + -0.9375 + 0.5t + t2 = 0 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + 0.5t + t2 = 0 + -0.9375 0.5t + t2 = 0 + -0.9375 Combine like terms: 0 + -0.9375 = -0.9375 0.5t + t2 = -0.9375 The t term is 0.5t. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5t + 0.0625 + t2 = -0.9375 + 0.0625 Reorder the terms: 0.0625 + 0.5t + t2 = -0.9375 + 0.0625 Combine like terms: -0.9375 + 0.0625 = -0.875 0.0625 + 0.5t + t2 = -0.875 Factor a perfect square on the left side: (t + 0.25)(t + 0.25) = -0.875 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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