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Simplifying 0 = -16t2 + 64t + 300 Reorder the terms: 0 = 300 + 64t + -16t2 Solving 0 = 300 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -300 = -300 -300 + -64t + 16t2 = 300 + 64t + -16t2 + -300 + -64t + 16t2 Reorder the terms: -300 + -64t + 16t2 = 300 + -300 + 64t + -64t + -16t2 + 16t2 Combine like terms: 300 + -300 = 0 -300 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -300 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -300 + -64t + 16t2 = 0 + -16t2 + 16t2 -300 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -300 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-75 + -16t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-75 + -16t + 4t2)' equal to zero and attempt to solve: Simplifying -75 + -16t + 4t2 = 0 Solving -75 + -16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + -4t + t2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -4t + 18.75 + t2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -4t + t2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -4t + t2 = 0 + 18.75 -4t + t2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -4t + t2 = 18.75 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 18.75 + 4 Reorder the terms: 4 + -4t + t2 = 18.75 + 4 Combine like terms: 18.75 + 4 = 22.75 4 + -4t + t2 = 22.75 Factor a perfect square on the left side: (t + -2)(t + -2) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (t + -2) equal to 4.769696007 and -4.769696007.Subproblem 1
t + -2 = 4.769696007 Simplifying t + -2 = 4.769696007 Reorder the terms: -2 + t = 4.769696007 Solving -2 + t = 4.769696007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 4.769696007 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.769696007 + 2 t = 4.769696007 + 2 Combine like terms: 4.769696007 + 2 = 6.769696007 t = 6.769696007 Simplifying t = 6.769696007Subproblem 2
t + -2 = -4.769696007 Simplifying t + -2 = -4.769696007 Reorder the terms: -2 + t = -4.769696007 Solving -2 + t = -4.769696007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -4.769696007 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.769696007 + 2 t = -4.769696007 + 2 Combine like terms: -4.769696007 + 2 = -2.769696007 t = -2.769696007 Simplifying t = -2.769696007Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.769696007, -2.769696007}Solution
t = {6.769696007, -2.769696007}
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