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Simplifying 0 = 16t2 + 10t + 100 Reorder the terms: 0 = 100 + 10t + 16t2 Solving 0 = 100 + 10t + 16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -10t + -16t2 = 100 + 10t + 16t2 + -100 + -10t + -16t2 Reorder the terms: -100 + -10t + -16t2 = 100 + -100 + 10t + -10t + 16t2 + -16t2 Combine like terms: 100 + -100 = 0 -100 + -10t + -16t2 = 0 + 10t + -10t + 16t2 + -16t2 -100 + -10t + -16t2 = 10t + -10t + 16t2 + -16t2 Combine like terms: 10t + -10t = 0 -100 + -10t + -16t2 = 0 + 16t2 + -16t2 -100 + -10t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -100 + -10t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(50 + 5t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(50 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying 50 + 5t + 8t2 = 0 Solving 50 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.25 + 0.625t + t2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 0.625t + -6.25 + t2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 0.625t + t2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 0.625t + t2 = 0 + -6.25 0.625t + t2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 0.625t + t2 = -6.25 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = -6.25 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = -6.25 + 0.09765625 Combine like terms: -6.25 + 0.09765625 = -6.15234375 0.09765625 + 0.625t + t2 = -6.15234375 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = -6.15234375 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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