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Simplifying 0 = -16t2 + 8t + 2 Reorder the terms: 0 = 2 + 8t + -16t2 Solving 0 = 2 + 8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -8t + 16t2 = 2 + 8t + -16t2 + -2 + -8t + 16t2 Reorder the terms: -2 + -8t + 16t2 = 2 + -2 + 8t + -8t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 -2 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 -2 + -8t + 16t2 = 0 + -16t2 + 16t2 -2 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -4t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4t + 8t2)' equal to zero and attempt to solve: Simplifying -1 + -4t + 8t2 = 0 Solving -1 + -4t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.5t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.5t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.5t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.5t + t2 = 0 + 0.125 -0.5t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.5t + t2 = 0.125 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 0.125 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 0.125 + 0.0625 Combine like terms: 0.125 + 0.0625 = 0.1875 0.0625 + -0.5t + t2 = 0.1875 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (t + -0.25) equal to 0.433012702 and -0.433012702.Subproblem 1
t + -0.25 = 0.433012702 Simplifying t + -0.25 = 0.433012702 Reorder the terms: -0.25 + t = 0.433012702 Solving -0.25 + t = 0.433012702 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 0.433012702 + 0.25 t = 0.433012702 + 0.25 Combine like terms: 0.433012702 + 0.25 = 0.683012702 t = 0.683012702 Simplifying t = 0.683012702Subproblem 2
t + -0.25 = -0.433012702 Simplifying t + -0.25 = -0.433012702 Reorder the terms: -0.25 + t = -0.433012702 Solving -0.25 + t = -0.433012702 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -0.433012702 + 0.25 t = -0.433012702 + 0.25 Combine like terms: -0.433012702 + 0.25 = -0.183012702 t = -0.183012702 Simplifying t = -0.183012702Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.683012702, -0.183012702}Solution
t = {0.683012702, -0.183012702}
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