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Simplifying -16t2 + 34t + 4 = 0 Reorder the terms: 4 + 34t + -16t2 = 0 Solving 4 + 34t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 17t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 17t + -8t2)' equal to zero and attempt to solve: Simplifying 2 + 17t + -8t2 = 0 Solving 2 + 17t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.25 + -2.125t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.125t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.125t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.125t + t2 = 0 + 0.25 -2.125t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.125t + t2 = 0.25 The t term is -2.125t. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125t + 1.12890625 + t2 = 0.25 + 1.12890625 Reorder the terms: 1.12890625 + -2.125t + t2 = 0.25 + 1.12890625 Combine like terms: 0.25 + 1.12890625 = 1.37890625 1.12890625 + -2.125t + t2 = 1.37890625 Factor a perfect square on the left side: (t + -1.0625)(t + -1.0625) = 1.37890625 Calculate the square root of the right side: 1.174268389 Break this problem into two subproblems by setting (t + -1.0625) equal to 1.174268389 and -1.174268389.Subproblem 1
t + -1.0625 = 1.174268389 Simplifying t + -1.0625 = 1.174268389 Reorder the terms: -1.0625 + t = 1.174268389 Solving -1.0625 + t = 1.174268389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = 1.174268389 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = 1.174268389 + 1.0625 t = 1.174268389 + 1.0625 Combine like terms: 1.174268389 + 1.0625 = 2.236768389 t = 2.236768389 Simplifying t = 2.236768389Subproblem 2
t + -1.0625 = -1.174268389 Simplifying t + -1.0625 = -1.174268389 Reorder the terms: -1.0625 + t = -1.174268389 Solving -1.0625 + t = -1.174268389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = -1.174268389 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = -1.174268389 + 1.0625 t = -1.174268389 + 1.0625 Combine like terms: -1.174268389 + 1.0625 = -0.111768389 t = -0.111768389 Simplifying t = -0.111768389Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.236768389, -0.111768389}Solution
t = {2.236768389, -0.111768389}
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