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Simplifying -16t2 + 10t + 100 = 0 Reorder the terms: 100 + 10t + -16t2 = 0 Solving 100 + 10t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 5t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 5t + -8t2)' equal to zero and attempt to solve: Simplifying 50 + 5t + -8t2 = 0 Solving 50 + 5t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6.25 + -0.625t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -0.625t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -0.625t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -0.625t + t2 = 0 + 6.25 -0.625t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -0.625t + t2 = 6.25 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 = 6.25 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 6.25 + 0.09765625 Combine like terms: 6.25 + 0.09765625 = 6.34765625 0.09765625 + -0.625t + t2 = 6.34765625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 6.34765625 Calculate the square root of the right side: 2.519455546 Break this problem into two subproblems by setting (t + -0.3125) equal to 2.519455546 and -2.519455546.Subproblem 1
t + -0.3125 = 2.519455546 Simplifying t + -0.3125 = 2.519455546 Reorder the terms: -0.3125 + t = 2.519455546 Solving -0.3125 + t = 2.519455546 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 = 2.519455546 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 2.519455546 + 0.3125 t = 2.519455546 + 0.3125 Combine like terms: 2.519455546 + 0.3125 = 2.831955546 t = 2.831955546 Simplifying t = 2.831955546Subproblem 2
t + -0.3125 = -2.519455546 Simplifying t + -0.3125 = -2.519455546 Reorder the terms: -0.3125 + t = -2.519455546 Solving -0.3125 + t = -2.519455546 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 = -2.519455546 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -2.519455546 + 0.3125 t = -2.519455546 + 0.3125 Combine like terms: -2.519455546 + 0.3125 = -2.206955546 t = -2.206955546 Simplifying t = -2.206955546Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.831955546, -2.206955546}Solution
t = {2.831955546, -2.206955546}
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