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Simplifying 130 = -16t2 + 40t + 104 Reorder the terms: 130 = 104 + 40t + -16t2 Solving 130 = 104 + 40t + -16t2 Solving for variable 't'. Combine like terms: 130 + -104 = 26 26 + -40t + 16t2 = 104 + 40t + -16t2 + -104 + -40t + 16t2 Reorder the terms: 26 + -40t + 16t2 = 104 + -104 + 40t + -40t + -16t2 + 16t2 Combine like terms: 104 + -104 = 0 26 + -40t + 16t2 = 0 + 40t + -40t + -16t2 + 16t2 26 + -40t + 16t2 = 40t + -40t + -16t2 + 16t2 Combine like terms: 40t + -40t = 0 26 + -40t + 16t2 = 0 + -16t2 + 16t2 26 + -40t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 26 + -40t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -20t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -20t + 8t2)' equal to zero and attempt to solve: Simplifying 13 + -20t + 8t2 = 0 Solving 13 + -20t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.625 + -2.5t + t2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -2.5t + -1.625 + t2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -2.5t + t2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -2.5t + t2 = 0 + -1.625 -2.5t + t2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -2.5t + t2 = -1.625 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = -1.625 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = -1.625 + 1.5625 Combine like terms: -1.625 + 1.5625 = -0.0625 1.5625 + -2.5t + t2 = -0.0625 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = -0.0625 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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