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Simplifying -16t2 + 128t + 155 = 0 Reorder the terms: 155 + 128t + -16t2 = 0 Solving 155 + 128t + -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'. -9.6875 + -8t + t2 = 0 Move the constant term to the right: Add '9.6875' to each side of the equation. -9.6875 + -8t + 9.6875 + t2 = 0 + 9.6875 Reorder the terms: -9.6875 + 9.6875 + -8t + t2 = 0 + 9.6875 Combine like terms: -9.6875 + 9.6875 = 0.0000 0.0000 + -8t + t2 = 0 + 9.6875 -8t + t2 = 0 + 9.6875 Combine like terms: 0 + 9.6875 = 9.6875 -8t + t2 = 9.6875 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 9.6875 + 16 Reorder the terms: 16 + -8t + t2 = 9.6875 + 16 Combine like terms: 9.6875 + 16 = 25.6875 16 + -8t + t2 = 25.6875 Factor a perfect square on the left side: (t + -4)(t + -4) = 25.6875 Calculate the square root of the right side: 5.068283733 Break this problem into two subproblems by setting (t + -4) equal to 5.068283733 and -5.068283733.Subproblem 1
t + -4 = 5.068283733 Simplifying t + -4 = 5.068283733 Reorder the terms: -4 + t = 5.068283733 Solving -4 + t = 5.068283733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 5.068283733 + 4 Combine like terms: -4 + 4 = 0 0 + t = 5.068283733 + 4 t = 5.068283733 + 4 Combine like terms: 5.068283733 + 4 = 9.068283733 t = 9.068283733 Simplifying t = 9.068283733Subproblem 2
t + -4 = -5.068283733 Simplifying t + -4 = -5.068283733 Reorder the terms: -4 + t = -5.068283733 Solving -4 + t = -5.068283733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -5.068283733 + 4 Combine like terms: -4 + 4 = 0 0 + t = -5.068283733 + 4 t = -5.068283733 + 4 Combine like terms: -5.068283733 + 4 = -1.068283733 t = -1.068283733 Simplifying t = -1.068283733Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.068283733, -1.068283733}
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