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Simplifying -16t2 + 50t + 2 = 0 Reorder the terms: 2 + 50t + -16t2 = 0 Solving 2 + 50t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 25t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 25t + -8t2)' equal to zero and attempt to solve: Simplifying 1 + 25t + -8t2 = 0 Solving 1 + 25t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -3.125t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -3.125t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -3.125t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -3.125t + t2 = 0 + 0.125 -3.125t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -3.125t + t2 = 0.125 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 = 0.125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 0.125 + 2.44140625 Combine like terms: 0.125 + 2.44140625 = 2.56640625 2.44140625 + -3.125t + t2 = 2.56640625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 2.56640625 Calculate the square root of the right side: 1.602000702 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.602000702 and -1.602000702.Subproblem 1
t + -1.5625 = 1.602000702 Simplifying t + -1.5625 = 1.602000702 Reorder the terms: -1.5625 + t = 1.602000702 Solving -1.5625 + t = 1.602000702 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 = 1.602000702 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.602000702 + 1.5625 t = 1.602000702 + 1.5625 Combine like terms: 1.602000702 + 1.5625 = 3.164500702 t = 3.164500702 Simplifying t = 3.164500702Subproblem 2
t + -1.5625 = -1.602000702 Simplifying t + -1.5625 = -1.602000702 Reorder the terms: -1.5625 + t = -1.602000702 Solving -1.5625 + t = -1.602000702 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 = -1.602000702 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.602000702 + 1.5625 t = -1.602000702 + 1.5625 Combine like terms: -1.602000702 + 1.5625 = -0.039500702 t = -0.039500702 Simplifying t = -0.039500702Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.164500702, -0.039500702}Solution
t = {3.164500702, -0.039500702}
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