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Simplifying -16t2 + 10t + 36 = 0 Reorder the terms: 36 + 10t + -16t2 = 0 Solving 36 + 10t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + 5t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + 5t + -8t2)' equal to zero and attempt to solve: Simplifying 18 + 5t + -8t2 = 0 Solving 18 + 5t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.25 + -0.625t + t2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.625t + 2.25 + t2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.625t + t2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.625t + t2 = 0 + 2.25 -0.625t + t2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.625t + t2 = 2.25 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 = 2.25 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 2.25 + 0.09765625 Combine like terms: 2.25 + 0.09765625 = 2.34765625 0.09765625 + -0.625t + t2 = 2.34765625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 2.34765625 Calculate the square root of the right side: 1.532206334 Break this problem into two subproblems by setting (t + -0.3125) equal to 1.532206334 and -1.532206334.Subproblem 1
t + -0.3125 = 1.532206334 Simplifying t + -0.3125 = 1.532206334 Reorder the terms: -0.3125 + t = 1.532206334 Solving -0.3125 + t = 1.532206334 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 = 1.532206334 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 1.532206334 + 0.3125 t = 1.532206334 + 0.3125 Combine like terms: 1.532206334 + 0.3125 = 1.844706334 t = 1.844706334 Simplifying t = 1.844706334Subproblem 2
t + -0.3125 = -1.532206334 Simplifying t + -0.3125 = -1.532206334 Reorder the terms: -0.3125 + t = -1.532206334 Solving -0.3125 + t = -1.532206334 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 = -1.532206334 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -1.532206334 + 0.3125 t = -1.532206334 + 0.3125 Combine like terms: -1.532206334 + 0.3125 = -1.219706334 t = -1.219706334 Simplifying t = -1.219706334Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.844706334, -1.219706334}Solution
t = {1.844706334, -1.219706334}
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