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Simplifying -16t2 + 5t + -2 = 20t Reorder the terms: -2 + 5t + -16t2 = 20t Solving -2 + 5t + -16t2 = 20t Solving for variable 't'. Reorder the terms: -2 + 5t + -20t + -16t2 = 20t + -20t Combine like terms: 5t + -20t = -15t -2 + -15t + -16t2 = 20t + -20t Combine like terms: 20t + -20t = 0 -2 + -15t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 15t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 15t + 16t2)' equal to zero and attempt to solve: Simplifying 2 + 15t + 16t2 = 0 Solving 2 + 15t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.125 + 0.9375t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 0.9375t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 0.9375t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 0.9375t + t2 = 0 + -0.125 0.9375t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 0.9375t + t2 = -0.125 The t term is 0.9375t. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375t + 0.2197265625 + t2 = -0.125 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = -0.125 + 0.2197265625 Combine like terms: -0.125 + 0.2197265625 = 0.0947265625 0.2197265625 + 0.9375t + t2 = 0.0947265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 0.0947265625 Calculate the square root of the right side: 0.307776806 Break this problem into two subproblems by setting (t + 0.46875) equal to 0.307776806 and -0.307776806.Subproblem 1
t + 0.46875 = 0.307776806 Simplifying t + 0.46875 = 0.307776806 Reorder the terms: 0.46875 + t = 0.307776806 Solving 0.46875 + t = 0.307776806 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = 0.307776806 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 0.307776806 + -0.46875 t = 0.307776806 + -0.46875 Combine like terms: 0.307776806 + -0.46875 = -0.160973194 t = -0.160973194 Simplifying t = -0.160973194Subproblem 2
t + 0.46875 = -0.307776806 Simplifying t + 0.46875 = -0.307776806 Reorder the terms: 0.46875 + t = -0.307776806 Solving 0.46875 + t = -0.307776806 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = -0.307776806 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -0.307776806 + -0.46875 t = -0.307776806 + -0.46875 Combine like terms: -0.307776806 + -0.46875 = -0.776526806 t = -0.776526806 Simplifying t = -0.776526806Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.160973194, -0.776526806}Solution
t = {-0.160973194, -0.776526806}
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