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Simplifying 16t2 + 256t + 80 = 0 Reorder the terms: 80 + 256t + 16t2 = 0 Solving 80 + 256t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(5 + 16t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(5 + 16t + t2)' equal to zero and attempt to solve: Simplifying 5 + 16t + t2 = 0 Solving 5 + 16t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 16t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + 16t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 16t + t2 = 0 + -5 16t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 16t + t2 = -5 The t term is 16t. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16t + 64 + t2 = -5 + 64 Reorder the terms: 64 + 16t + t2 = -5 + 64 Combine like terms: -5 + 64 = 59 64 + 16t + t2 = 59 Factor a perfect square on the left side: (t + 8)(t + 8) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (t + 8) equal to 7.681145748 and -7.681145748.Subproblem 1
t + 8 = 7.681145748 Simplifying t + 8 = 7.681145748 Reorder the terms: 8 + t = 7.681145748 Solving 8 + t = 7.681145748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 7.681145748 + -8 Combine like terms: 8 + -8 = 0 0 + t = 7.681145748 + -8 t = 7.681145748 + -8 Combine like terms: 7.681145748 + -8 = -0.318854252 t = -0.318854252 Simplifying t = -0.318854252Subproblem 2
t + 8 = -7.681145748 Simplifying t + 8 = -7.681145748 Reorder the terms: 8 + t = -7.681145748 Solving 8 + t = -7.681145748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = -7.681145748 + -8 Combine like terms: 8 + -8 = 0 0 + t = -7.681145748 + -8 t = -7.681145748 + -8 Combine like terms: -7.681145748 + -8 = -15.681145748 t = -15.681145748 Simplifying t = -15.681145748Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.318854252, -15.681145748}Solution
t = {-0.318854252, -15.681145748}
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