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Simplifying 93 = 210t + -16t2 Solving 93 = 210t + -16t2 Solving for variable 't'. Reorder the terms: 93 + -210t + 16t2 = 210t + -210t + -16t2 + 16t2 Combine like terms: 210t + -210t = 0 93 + -210t + 16t2 = 0 + -16t2 + 16t2 93 + -210t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 93 + -210t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.8125 + -13.125t + t2 = 0 Move the constant term to the right: Add '-5.8125' to each side of the equation. 5.8125 + -13.125t + -5.8125 + t2 = 0 + -5.8125 Reorder the terms: 5.8125 + -5.8125 + -13.125t + t2 = 0 + -5.8125 Combine like terms: 5.8125 + -5.8125 = 0.0000 0.0000 + -13.125t + t2 = 0 + -5.8125 -13.125t + t2 = 0 + -5.8125 Combine like terms: 0 + -5.8125 = -5.8125 -13.125t + t2 = -5.8125 The t term is -13.125t. Take half its coefficient (-6.5625). Square it (43.06640625) and add it to both sides. Add '43.06640625' to each side of the equation. -13.125t + 43.06640625 + t2 = -5.8125 + 43.06640625 Reorder the terms: 43.06640625 + -13.125t + t2 = -5.8125 + 43.06640625 Combine like terms: -5.8125 + 43.06640625 = 37.25390625 43.06640625 + -13.125t + t2 = 37.25390625 Factor a perfect square on the left side: (t + -6.5625)(t + -6.5625) = 37.25390625 Calculate the square root of the right side: 6.103597812 Break this problem into two subproblems by setting (t + -6.5625) equal to 6.103597812 and -6.103597812.Subproblem 1
t + -6.5625 = 6.103597812 Simplifying t + -6.5625 = 6.103597812 Reorder the terms: -6.5625 + t = 6.103597812 Solving -6.5625 + t = 6.103597812 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5625' to each side of the equation. -6.5625 + 6.5625 + t = 6.103597812 + 6.5625 Combine like terms: -6.5625 + 6.5625 = 0.0000 0.0000 + t = 6.103597812 + 6.5625 t = 6.103597812 + 6.5625 Combine like terms: 6.103597812 + 6.5625 = 12.666097812 t = 12.666097812 Simplifying t = 12.666097812Subproblem 2
t + -6.5625 = -6.103597812 Simplifying t + -6.5625 = -6.103597812 Reorder the terms: -6.5625 + t = -6.103597812 Solving -6.5625 + t = -6.103597812 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.5625' to each side of the equation. -6.5625 + 6.5625 + t = -6.103597812 + 6.5625 Combine like terms: -6.5625 + 6.5625 = 0.0000 0.0000 + t = -6.103597812 + 6.5625 t = -6.103597812 + 6.5625 Combine like terms: -6.103597812 + 6.5625 = 0.458902188 t = 0.458902188 Simplifying t = 0.458902188Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.666097812, 0.458902188}
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