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Simplifying 80 = 24t + -10t2 Solving 80 = 24t + -10t2 Solving for variable 't'. Reorder the terms: 80 + -24t + 10t2 = 24t + -24t + -10t2 + 10t2 Combine like terms: 24t + -24t = 0 80 + -24t + 10t2 = 0 + -10t2 + 10t2 80 + -24t + 10t2 = -10t2 + 10t2 Combine like terms: -10t2 + 10t2 = 0 80 + -24t + 10t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -12t + 5t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -12t + 5t2)' equal to zero and attempt to solve: Simplifying 40 + -12t + 5t2 = 0 Solving 40 + -12t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8 + -2.4t + t2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -2.4t + -8 + t2 = 0 + -8 Reorder the terms: 8 + -8 + -2.4t + t2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -2.4t + t2 = 0 + -8 -2.4t + t2 = 0 + -8 Combine like terms: 0 + -8 = -8 -2.4t + t2 = -8 The t term is -2.4t. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4t + 1.44 + t2 = -8 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = -8 + 1.44 Combine like terms: -8 + 1.44 = -6.56 1.44 + -2.4t + t2 = -6.56 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = -6.56 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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