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Simplifying -16t2 + -50t + 80 = 0 Reorder the terms: 80 + -50t + -16t2 = 0 Solving 80 + -50t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(40 + -25t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(40 + -25t + -8t2)' equal to zero and attempt to solve: Simplifying 40 + -25t + -8t2 = 0 Solving 40 + -25t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -5 + 3.125t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.125t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + 3.125t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.125t + t2 = 0 + 5 3.125t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.125t + t2 = 5 The t term is 3.125t. Take half its coefficient (1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. 3.125t + 2.44140625 + t2 = 5 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = 5 + 2.44140625 Combine like terms: 5 + 2.44140625 = 7.44140625 2.44140625 + 3.125t + t2 = 7.44140625 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = 7.44140625 Calculate the square root of the right side: 2.727894105 Break this problem into two subproblems by setting (t + 1.5625) equal to 2.727894105 and -2.727894105.Subproblem 1
t + 1.5625 = 2.727894105 Simplifying t + 1.5625 = 2.727894105 Reorder the terms: 1.5625 + t = 2.727894105 Solving 1.5625 + t = 2.727894105 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = 2.727894105 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = 2.727894105 + -1.5625 t = 2.727894105 + -1.5625 Combine like terms: 2.727894105 + -1.5625 = 1.165394105 t = 1.165394105 Simplifying t = 1.165394105Subproblem 2
t + 1.5625 = -2.727894105 Simplifying t + 1.5625 = -2.727894105 Reorder the terms: 1.5625 + t = -2.727894105 Solving 1.5625 + t = -2.727894105 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5625' to each side of the equation. 1.5625 + -1.5625 + t = -2.727894105 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = -2.727894105 + -1.5625 t = -2.727894105 + -1.5625 Combine like terms: -2.727894105 + -1.5625 = -4.290394105 t = -4.290394105 Simplifying t = -4.290394105Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.165394105, -4.290394105}Solution
t = {1.165394105, -4.290394105}
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