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Simplifying 0 = 154 + -10t + -16t2 Solving 0 = 154 + -10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -154 = -154 -154 + 10t + 16t2 = 154 + -10t + -16t2 + -154 + 10t + 16t2 Reorder the terms: -154 + 10t + 16t2 = 154 + -154 + -10t + 10t + -16t2 + 16t2 Combine like terms: 154 + -154 = 0 -154 + 10t + 16t2 = 0 + -10t + 10t + -16t2 + 16t2 -154 + 10t + 16t2 = -10t + 10t + -16t2 + 16t2 Combine like terms: -10t + 10t = 0 -154 + 10t + 16t2 = 0 + -16t2 + 16t2 -154 + 10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -154 + 10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-77 + 5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-77 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying -77 + 5t + 8t2 = 0 Solving -77 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9.625 + 0.625t + t2 = 0 Move the constant term to the right: Add '9.625' to each side of the equation. -9.625 + 0.625t + 9.625 + t2 = 0 + 9.625 Reorder the terms: -9.625 + 9.625 + 0.625t + t2 = 0 + 9.625 Combine like terms: -9.625 + 9.625 = 0.000 0.000 + 0.625t + t2 = 0 + 9.625 0.625t + t2 = 0 + 9.625 Combine like terms: 0 + 9.625 = 9.625 0.625t + t2 = 9.625 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 9.625 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 9.625 + 0.09765625 Combine like terms: 9.625 + 0.09765625 = 9.72265625 0.09765625 + 0.625t + t2 = 9.72265625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 9.72265625 Calculate the square root of the right side: 3.118117421 Break this problem into two subproblems by setting (t + 0.3125) equal to 3.118117421 and -3.118117421.Subproblem 1
t + 0.3125 = 3.118117421 Simplifying t + 0.3125 = 3.118117421 Reorder the terms: 0.3125 + t = 3.118117421 Solving 0.3125 + t = 3.118117421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 3.118117421 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 3.118117421 + -0.3125 t = 3.118117421 + -0.3125 Combine like terms: 3.118117421 + -0.3125 = 2.805617421 t = 2.805617421 Simplifying t = 2.805617421Subproblem 2
t + 0.3125 = -3.118117421 Simplifying t + 0.3125 = -3.118117421 Reorder the terms: 0.3125 + t = -3.118117421 Solving 0.3125 + t = -3.118117421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -3.118117421 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -3.118117421 + -0.3125 t = -3.118117421 + -0.3125 Combine like terms: -3.118117421 + -0.3125 = -3.430617421 t = -3.430617421 Simplifying t = -3.430617421Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.805617421, -3.430617421}Solution
t = {2.805617421, -3.430617421}
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