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Simplifying 0 = -16t2 + 16t + 10 Reorder the terms: 0 = 10 + 16t + -16t2 Solving 0 = 10 + 16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -16t + 16t2 = 10 + 16t + -16t2 + -10 + -16t + 16t2 Reorder the terms: -10 + -16t + 16t2 = 10 + -10 + 16t + -16t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -10 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -10 + -16t + 16t2 = 0 + -16t2 + 16t2 -10 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -8t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -8t + 8t2)' equal to zero and attempt to solve: Simplifying -5 + -8t + 8t2 = 0 Solving -5 + -8t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -1t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1t + t2 = 0 + 0.625 -1t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1t + t2 = 0.625 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 0.625 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 0.625 + 0.25 Combine like terms: 0.625 + 0.25 = 0.875 0.25 + -1t + t2 = 0.875 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (t + -0.5) equal to 0.935414347 and -0.935414347.Subproblem 1
t + -0.5 = 0.935414347 Simplifying t + -0.5 = 0.935414347 Reorder the terms: -0.5 + t = 0.935414347 Solving -0.5 + t = 0.935414347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.935414347 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.935414347 + 0.5 t = 0.935414347 + 0.5 Combine like terms: 0.935414347 + 0.5 = 1.435414347 t = 1.435414347 Simplifying t = 1.435414347Subproblem 2
t + -0.5 = -0.935414347 Simplifying t + -0.5 = -0.935414347 Reorder the terms: -0.5 + t = -0.935414347 Solving -0.5 + t = -0.935414347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.935414347 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.935414347 + 0.5 t = -0.935414347 + 0.5 Combine like terms: -0.935414347 + 0.5 = -0.435414347 t = -0.435414347 Simplifying t = -0.435414347Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.435414347, -0.435414347}Solution
t = {1.435414347, -0.435414347}
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