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Simplifying 0 = -16t2 + 64t + 155 Reorder the terms: 0 = 155 + 64t + -16t2 Solving 0 = 155 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -155 = -155 -155 + -64t + 16t2 = 155 + 64t + -16t2 + -155 + -64t + 16t2 Reorder the terms: -155 + -64t + 16t2 = 155 + -155 + 64t + -64t + -16t2 + 16t2 Combine like terms: 155 + -155 = 0 -155 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -155 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -155 + -64t + 16t2 = 0 + -16t2 + 16t2 -155 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -155 + -64t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9.6875 + -4t + t2 = 0 Move the constant term to the right: Add '9.6875' to each side of the equation. -9.6875 + -4t + 9.6875 + t2 = 0 + 9.6875 Reorder the terms: -9.6875 + 9.6875 + -4t + t2 = 0 + 9.6875 Combine like terms: -9.6875 + 9.6875 = 0.0000 0.0000 + -4t + t2 = 0 + 9.6875 -4t + t2 = 0 + 9.6875 Combine like terms: 0 + 9.6875 = 9.6875 -4t + t2 = 9.6875 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 = 9.6875 + 4 Reorder the terms: 4 + -4t + t2 = 9.6875 + 4 Combine like terms: 9.6875 + 4 = 13.6875 4 + -4t + t2 = 13.6875 Factor a perfect square on the left side: (t + -2)(t + -2) = 13.6875 Calculate the square root of the right side: 3.699662147 Break this problem into two subproblems by setting (t + -2) equal to 3.699662147 and -3.699662147.Subproblem 1
t + -2 = 3.699662147 Simplifying t + -2 = 3.699662147 Reorder the terms: -2 + t = 3.699662147 Solving -2 + t = 3.699662147 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 = 3.699662147 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.699662147 + 2 t = 3.699662147 + 2 Combine like terms: 3.699662147 + 2 = 5.699662147 t = 5.699662147 Simplifying t = 5.699662147Subproblem 2
t + -2 = -3.699662147 Simplifying t + -2 = -3.699662147 Reorder the terms: -2 + t = -3.699662147 Solving -2 + t = -3.699662147 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 = -3.699662147 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.699662147 + 2 t = -3.699662147 + 2 Combine like terms: -3.699662147 + 2 = -1.699662147 t = -1.699662147 Simplifying t = -1.699662147Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.699662147, -1.699662147}
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