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Simplifying -16t2 + 40t + 10 = 0 Reorder the terms: 10 + 40t + -16t2 = 0 Solving 10 + 40t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 20t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 20t + -8t2)' equal to zero and attempt to solve: Simplifying 5 + 20t + -8t2 = 0 Solving 5 + 20t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -2.5t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2.5t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2.5t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2.5t + t2 = 0 + 0.625 -2.5t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2.5t + t2 = 0.625 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = 0.625 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 0.625 + 1.5625 Combine like terms: 0.625 + 1.5625 = 2.1875 1.5625 + -2.5t + t2 = 2.1875 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 2.1875 Calculate the square root of the right side: 1.479019946 Break this problem into two subproblems by setting (t + -1.25) equal to 1.479019946 and -1.479019946.Subproblem 1
t + -1.25 = 1.479019946 Simplifying t + -1.25 = 1.479019946 Reorder the terms: -1.25 + t = 1.479019946 Solving -1.25 + t = 1.479019946 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 1.479019946 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 1.479019946 + 1.25 t = 1.479019946 + 1.25 Combine like terms: 1.479019946 + 1.25 = 2.729019946 t = 2.729019946 Simplifying t = 2.729019946Subproblem 2
t + -1.25 = -1.479019946 Simplifying t + -1.25 = -1.479019946 Reorder the terms: -1.25 + t = -1.479019946 Solving -1.25 + t = -1.479019946 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -1.479019946 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -1.479019946 + 1.25 t = -1.479019946 + 1.25 Combine like terms: -1.479019946 + 1.25 = -0.229019946 t = -0.229019946 Simplifying t = -0.229019946Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.729019946, -0.229019946}Solution
t = {2.729019946, -0.229019946}
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