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Simplifying -16t2 + 8.726330923t + 1.5 = 0 Reorder the terms: 1.5 + 8.726330923t + -16t2 = 0 Solving 1.5 + 8.726330923t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.09375 + -0.5453956827t + t2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + -0.5453956827t + 0.09375 + t2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + -0.5453956827t + t2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + -0.5453956827t + t2 = 0 + 0.09375 -0.5453956827t + t2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 -0.5453956827t + t2 = 0.09375 The t term is -0.5453956827t. Take half its coefficient (-0.2726978414). Square it (0.07436411270) and add it to both sides. Add '0.07436411270' to each side of the equation. -0.5453956827t + 0.07436411270 + t2 = 0.09375 + 0.07436411270 Reorder the terms: 0.07436411270 + -0.5453956827t + t2 = 0.09375 + 0.07436411270 Combine like terms: 0.09375 + 0.07436411270 = 0.1681141127 0.07436411270 + -0.5453956827t + t2 = 0.1681141127 Factor a perfect square on the left side: (t + -0.2726978414)(t + -0.2726978414) = 0.1681141127 Calculate the square root of the right side: 0.41001721 Break this problem into two subproblems by setting (t + -0.2726978414) equal to 0.41001721 and -0.41001721.Subproblem 1
t + -0.2726978414 = 0.41001721 Simplifying t + -0.2726978414 = 0.41001721 Reorder the terms: -0.2726978414 + t = 0.41001721 Solving -0.2726978414 + t = 0.41001721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2726978414' to each side of the equation. -0.2726978414 + 0.2726978414 + t = 0.41001721 + 0.2726978414 Combine like terms: -0.2726978414 + 0.2726978414 = 0.0000000000 0.0000000000 + t = 0.41001721 + 0.2726978414 t = 0.41001721 + 0.2726978414 Combine like terms: 0.41001721 + 0.2726978414 = 0.6827150514 t = 0.6827150514 Simplifying t = 0.6827150514Subproblem 2
t + -0.2726978414 = -0.41001721 Simplifying t + -0.2726978414 = -0.41001721 Reorder the terms: -0.2726978414 + t = -0.41001721 Solving -0.2726978414 + t = -0.41001721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2726978414' to each side of the equation. -0.2726978414 + 0.2726978414 + t = -0.41001721 + 0.2726978414 Combine like terms: -0.2726978414 + 0.2726978414 = 0.0000000000 0.0000000000 + t = -0.41001721 + 0.2726978414 t = -0.41001721 + 0.2726978414 Combine like terms: -0.41001721 + 0.2726978414 = -0.1373193686 t = -0.1373193686 Simplifying t = -0.1373193686Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6827150514, -0.1373193686}
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