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Simplifying 0 = -8t2 + -15t + 100 Reorder the terms: 0 = 100 + -15t + -8t2 Solving 0 = 100 + -15t + -8t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + 15t + 8t2 = 100 + -15t + -8t2 + -100 + 15t + 8t2 Reorder the terms: -100 + 15t + 8t2 = 100 + -100 + -15t + 15t + -8t2 + 8t2 Combine like terms: 100 + -100 = 0 -100 + 15t + 8t2 = 0 + -15t + 15t + -8t2 + 8t2 -100 + 15t + 8t2 = -15t + 15t + -8t2 + 8t2 Combine like terms: -15t + 15t = 0 -100 + 15t + 8t2 = 0 + -8t2 + 8t2 -100 + 15t + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 -100 + 15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -12.5 + 1.875t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.875t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.875t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.875t + t2 = 0 + 12.5 1.875t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.875t + t2 = 12.5 The t term is 1.875t. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875t + 0.87890625 + t2 = 12.5 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 12.5 + 0.87890625 Combine like terms: 12.5 + 0.87890625 = 13.37890625 0.87890625 + 1.875t + t2 = 13.37890625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 13.37890625 Calculate the square root of the right side: 3.657718722 Break this problem into two subproblems by setting (t + 0.9375) equal to 3.657718722 and -3.657718722.Subproblem 1
t + 0.9375 = 3.657718722 Simplifying t + 0.9375 = 3.657718722 Reorder the terms: 0.9375 + t = 3.657718722 Solving 0.9375 + t = 3.657718722 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = 3.657718722 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 3.657718722 + -0.9375 t = 3.657718722 + -0.9375 Combine like terms: 3.657718722 + -0.9375 = 2.720218722 t = 2.720218722 Simplifying t = 2.720218722Subproblem 2
t + 0.9375 = -3.657718722 Simplifying t + 0.9375 = -3.657718722 Reorder the terms: 0.9375 + t = -3.657718722 Solving 0.9375 + t = -3.657718722 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = -3.657718722 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -3.657718722 + -0.9375 t = -3.657718722 + -0.9375 Combine like terms: -3.657718722 + -0.9375 = -4.595218722 t = -4.595218722 Simplifying t = -4.595218722Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.720218722, -4.595218722}
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