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Simplifying -16t2 + 62t + 2 = 0 Reorder the terms: 2 + 62t + -16t2 = 0 Solving 2 + 62t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 31t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 31t + -8t2)' equal to zero and attempt to solve: Simplifying 1 + 31t + -8t2 = 0 Solving 1 + 31t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + -3.875t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -3.875t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -3.875t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -3.875t + t2 = 0 + 0.125 -3.875t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -3.875t + t2 = 0.125 The t term is -3.875t. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875t + 3.75390625 + t2 = 0.125 + 3.75390625 Reorder the terms: 3.75390625 + -3.875t + t2 = 0.125 + 3.75390625 Combine like terms: 0.125 + 3.75390625 = 3.87890625 3.75390625 + -3.875t + t2 = 3.87890625 Factor a perfect square on the left side: (t + -1.9375)(t + -1.9375) = 3.87890625 Calculate the square root of the right side: 1.969493907 Break this problem into two subproblems by setting (t + -1.9375) equal to 1.969493907 and -1.969493907.Subproblem 1
t + -1.9375 = 1.969493907 Simplifying t + -1.9375 = 1.969493907 Reorder the terms: -1.9375 + t = 1.969493907 Solving -1.9375 + t = 1.969493907 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = 1.969493907 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = 1.969493907 + 1.9375 t = 1.969493907 + 1.9375 Combine like terms: 1.969493907 + 1.9375 = 3.906993907 t = 3.906993907 Simplifying t = 3.906993907Subproblem 2
t + -1.9375 = -1.969493907 Simplifying t + -1.9375 = -1.969493907 Reorder the terms: -1.9375 + t = -1.969493907 Solving -1.9375 + t = -1.969493907 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = -1.969493907 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = -1.969493907 + 1.9375 t = -1.969493907 + 1.9375 Combine like terms: -1.969493907 + 1.9375 = -0.031993907 t = -0.031993907 Simplifying t = -0.031993907Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.906993907, -0.031993907}Solution
t = {3.906993907, -0.031993907}
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