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Simplifying -16t2 + 26t + 100 = 0 Reorder the terms: 100 + 26t + -16t2 = 0 Solving 100 + 26t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 13t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 13t + -8t2)' equal to zero and attempt to solve: Simplifying 50 + 13t + -8t2 = 0 Solving 50 + 13t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6.25 + -1.625t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -1.625t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -1.625t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -1.625t + t2 = 0 + 6.25 -1.625t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -1.625t + t2 = 6.25 The t term is -1.625t. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625t + 0.66015625 + t2 = 6.25 + 0.66015625 Reorder the terms: 0.66015625 + -1.625t + t2 = 6.25 + 0.66015625 Combine like terms: 6.25 + 0.66015625 = 6.91015625 0.66015625 + -1.625t + t2 = 6.91015625 Factor a perfect square on the left side: (t + -0.8125)(t + -0.8125) = 6.91015625 Calculate the square root of the right side: 2.628717606 Break this problem into two subproblems by setting (t + -0.8125) equal to 2.628717606 and -2.628717606.Subproblem 1
t + -0.8125 = 2.628717606 Simplifying t + -0.8125 = 2.628717606 Reorder the terms: -0.8125 + t = 2.628717606 Solving -0.8125 + t = 2.628717606 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + t = 2.628717606 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + t = 2.628717606 + 0.8125 t = 2.628717606 + 0.8125 Combine like terms: 2.628717606 + 0.8125 = 3.441217606 t = 3.441217606 Simplifying t = 3.441217606Subproblem 2
t + -0.8125 = -2.628717606 Simplifying t + -0.8125 = -2.628717606 Reorder the terms: -0.8125 + t = -2.628717606 Solving -0.8125 + t = -2.628717606 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + t = -2.628717606 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + t = -2.628717606 + 0.8125 t = -2.628717606 + 0.8125 Combine like terms: -2.628717606 + 0.8125 = -1.816217606 t = -1.816217606 Simplifying t = -1.816217606Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.441217606, -1.816217606}Solution
t = {3.441217606, -1.816217606}
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