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Simplifying -16t2 + -8t = 10 Reorder the terms: -8t + -16t2 = 10 Solving -8t + -16t2 = 10 Solving for variable 't'. Reorder the terms: -10 + -8t + -16t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -8t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 4t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 4t + 8t2)' equal to zero and attempt to solve: Simplifying 5 + 4t + 8t2 = 0 Solving 5 + 4t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 0.5t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 0.5t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 0.5t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 0.5t + t2 = 0 + -0.625 0.5t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 0.5t + t2 = -0.625 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 = -0.625 + 0.0625 Reorder the terms: 0.0625 + 0.5t + t2 = -0.625 + 0.0625 Combine like terms: -0.625 + 0.0625 = -0.5625 0.0625 + 0.5t + t2 = -0.5625 Factor a perfect square on the left side: (t + 0.25)(t + 0.25) = -0.5625 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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