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Simplifying 600 = -16t2 + 250t Reorder the terms: 600 = 250t + -16t2 Solving 600 = 250t + -16t2 Solving for variable 't'. Reorder the terms: 600 + -250t + 16t2 = 250t + -250t + -16t2 + 16t2 Combine like terms: 250t + -250t = 0 600 + -250t + 16t2 = 0 + -16t2 + 16t2 600 + -250t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 600 + -250t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(300 + -125t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(300 + -125t + 8t2)' equal to zero and attempt to solve: Simplifying 300 + -125t + 8t2 = 0 Solving 300 + -125t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 37.5 + -15.625t + t2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -15.625t + -37.5 + t2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -15.625t + t2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -15.625t + t2 = 0 + -37.5 -15.625t + t2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -15.625t + t2 = -37.5 The t term is -15.625t. Take half its coefficient (-7.8125). Square it (61.03515625) and add it to both sides. Add '61.03515625' to each side of the equation. -15.625t + 61.03515625 + t2 = -37.5 + 61.03515625 Reorder the terms: 61.03515625 + -15.625t + t2 = -37.5 + 61.03515625 Combine like terms: -37.5 + 61.03515625 = 23.53515625 61.03515625 + -15.625t + t2 = 23.53515625 Factor a perfect square on the left side: (t + -7.8125)(t + -7.8125) = 23.53515625 Calculate the square root of the right side: 4.851304593 Break this problem into two subproblems by setting (t + -7.8125) equal to 4.851304593 and -4.851304593.Subproblem 1
t + -7.8125 = 4.851304593 Simplifying t + -7.8125 = 4.851304593 Reorder the terms: -7.8125 + t = 4.851304593 Solving -7.8125 + t = 4.851304593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.8125' to each side of the equation. -7.8125 + 7.8125 + t = 4.851304593 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + t = 4.851304593 + 7.8125 t = 4.851304593 + 7.8125 Combine like terms: 4.851304593 + 7.8125 = 12.663804593 t = 12.663804593 Simplifying t = 12.663804593Subproblem 2
t + -7.8125 = -4.851304593 Simplifying t + -7.8125 = -4.851304593 Reorder the terms: -7.8125 + t = -4.851304593 Solving -7.8125 + t = -4.851304593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.8125' to each side of the equation. -7.8125 + 7.8125 + t = -4.851304593 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + t = -4.851304593 + 7.8125 t = -4.851304593 + 7.8125 Combine like terms: -4.851304593 + 7.8125 = 2.961195407 t = 2.961195407 Simplifying t = 2.961195407Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.663804593, 2.961195407}Solution
t = {12.663804593, 2.961195407}
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